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The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. Then the input and the output signals are uniquely given by their Laguerre spectra. It is shown that a discrete convolution operator with polynomial Markov parameters constitutes a common description of the delay operator in the continuous and discrete case. Closed-form expressions for the delay value in terms of the output and input Laguerre spectra are derived. The expressions hold for any feasible value of the Laguerre parameter and can be utilized for e.g. building time-delay estimators that allow for non-persistent input. A simulation example is provided to illustrate the principle of Laguerre-domain time-delay modeling and analysis with perfect disturbance rejection.

The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. Then the input and the output signals are uniquely given by their Laguerre spectra. It is shown that a discrete convolution operator with polynomial Markov parameters constitutes a common description of the delay operator in the continuous and discrete case. Closed-form expressions for the delay value in terms of the output and input Laguerre spectra are derived. The expressions hold for any feasible value of the Laguerre parameter and can be utilized for e.g. building time-delay estimators that allow for non-persistent input. A simulation example is provided to illustrate the principle of Laguerre-domain time-delay modeling and analysis with perfect disturbance rejection.

Active disturbance rejection control (ADRC) has been gaining attention in recent years and has shown its performance in multiple applications including non-linear ones, without the need of accurate models. Despite the good results of this technique, time delay can deteriorate the performance of ADRC, limiting its application. Here, the effect of time delay on the stability of a linear ADRC is analysed, using an alternative mathematical description, and a new effective design technique, based on a modified ADRC scheme, is proposed to overcome the delay effect while maintaining the disturbance rejection properties of the ADRC. An experimental example is discussed considering a system with low damped mechanical resonances, showing good results using the proposed technique.

[EN] This paper proposes an adaptive tuning method for the Linear-Quadratic FeedForward (LQ-FF) optimal controller. The procedure aims to reject disturbances while maintaining the reference tracking performance of the conventional LQ controller. The adaptive mechanism is formulated by analyzing each element of the control signal LQ-FF concerning state regulation, reference change, and disturbance compensation. The disturbance rejection mechanism is based on the classical strategy used in Proportional-IntegralDerivative controllers and the theoretical analysis studied in previous works for predictive controllers, which aim to obtain the inverse dynamics of the disturbances and process inputs in relation to the outputs. In addition, a comparison is presented between an augmented state space model and a model with a polynomial delay approximation for treating delays associated with disturbances and process inputs in the controller formulation. The proposed method effectively controls a validated nonlinear temperature system, maintaining performance equivalent to the conventional LQ controller for reference tracking while entirely rejecting disturbance effects. The proposed tuning achieves 10 % less output error, with an increase of only 18 % in the control effort compared to conventional tuning in simulations., [ES] Este trabajo propone un metodo de ajuste adaptativo para la metodología de control cuadrático lineal con acción de control por adelanto (LQ-FF, por sus siglas en inglés, Linear-Quadratic FeedForward). El metodo tiene como objetivo rechazar las perturbaciones al mismo tiempo que mantiene el desempeno de seguimiento a referencias del controlador LQ convencional. El mecanismo adaptativo se formula analizando cada elemento de la senal de control LQ-FF en relación con la regulación de estados, el cambio de referencia y la compensacion de perturbaciones. Además, el rechazo de perturbaciones se basa en los controladores Proporcional-Integral-Derivativo y el análisis teórico para controladores predictivos, los cuales tienen como objetivo obtener la dinámica inversa de las perturbaciones y las entradas del proceso. Se presenta una comparativa entre un modelo de espacio de estados aumentado y un modelo con aproximación de retardo polinomial para el tratamiento de los retardos asociados a las perturbaciones y las entradas del proceso en la formulacion del controlador. El método propuesto demuestra su eficacia en el control de un sistema de temperatura no lineal validado, manteniendo el rendimiento similar al controlador LQ convencional en el seguimiento de referencias y rechazando por completo los efectos de las perturbaciones. Para el escenario de simulacion presentado, la sintonía propuesta logra un 10 % menos de error de salida, con un incremento de solo un 18 % en el esfuerzo de control en comparacion con la sintonía convencional.

[EN] This paper proposes an adaptive tuning method for the Linear-Quadratic FeedForward (LQ-FF) optimal controller. The procedure aims to reject disturbances while maintaining the reference tracking performance of the conventional LQ controller. The adaptive mechanism is formulated by analyzing each element of the control signal LQ-FF concerning state regulation, reference change, and disturbance compensation. The disturbance rejection mechanism is based on the classical strategy used in Proportional-IntegralDerivative controllers and the theoretical analysis studied in previous works for predictive controllers, which aim to obtain the inverse dynamics of the disturbances and process inputs in relation to the outputs. In addition, a comparison is presented between an augmented state space model and a model with a polynomial delay approximation for treating delays associated with disturbances and process inputs in the controller formulation. The proposed method effectively controls a validated nonlinear temperature system, maintaining performance equivalent to the conventional LQ controller for reference tracking while entirely rejecting disturbance effects. The proposed tuning achieves 10 % less output error, with an increase of only 18 % in the control effort compared to conventional tuning in simulations., [ES] Este trabajo propone un metodo de ajuste adaptativo para la metodología de control cuadrático lineal con acción de control por adelanto (LQ-FF, por sus siglas en inglés, Linear-Quadratic FeedForward). El metodo tiene como objetivo rechazar las perturbaciones al mismo tiempo que mantiene el desempeno de seguimiento a referencias del controlador LQ convencional. El mecanismo adaptativo se formula analizando cada elemento de la senal de control LQ-FF en relación con la regulación de estados, el cambio de referencia y la compensacion de perturbaciones. Además, el rechazo de perturbaciones se basa en los controladores Proporcional-Integral-Derivativo y el análisis teórico para controladores predictivos, los cuales tienen como objetivo obtener la dinámica inversa de las perturbaciones y las entradas del proceso. Se presenta una comparativa entre un modelo de espacio de estados aumentado y un modelo con aproximación de retardo polinomial para el tratamiento de los retardos asociados a las perturbaciones y las entradas del proceso en la formulacion del controlador. El método propuesto demuestra su eficacia en el control de un sistema de temperatura no lineal validado, manteniendo el rendimiento similar al controlador LQ convencional en el seguimiento de referencias y rechazando por completo los efectos de las perturbaciones. Para el escenario de simulacion presentado, la sintonía propuesta logra un 10 % menos de error de salida, con un incremento de solo un 18 % en el esfuerzo de control en comparacion con la sintonía convencional.

[EN] This paper proposes an adaptive tuning method for the Linear-Quadratic FeedForward (LQ-FF) optimal controller. The procedure aims to reject disturbances while maintaining the reference tracking performance of the conventional LQ controller. The adaptive mechanism is formulated by analyzing each element of the control signal LQ-FF concerning state regulation, reference change, and disturbance compensation. The disturbance rejection mechanism is based on the classical strategy used in Proportional-IntegralDerivative controllers and the theoretical analysis studied in previous works for predictive controllers, which aim to obtain the inverse dynamics of the disturbances and process inputs in relation to the outputs. In addition, a comparison is presented between an augmented state space model and a model with a polynomial delay approximation for treating delays associated with disturbances and process inputs in the controller formulation. The proposed method effectively controls a validated nonlinear temperature system, maintaining performance equivalent to the conventional LQ controller for reference tracking while entirely rejecting disturbance effects. The proposed tuning achieves 10 % less output error, with an increase of only 18 % in the control effort compared to conventional tuning in simulations., [ES] Este trabajo propone un metodo de ajuste adaptativo para la metodología de control cuadrático lineal con acción de control por adelanto (LQ-FF, por sus siglas en inglés, Linear-Quadratic FeedForward). El metodo tiene como objetivo rechazar las perturbaciones al mismo tiempo que mantiene el desempeno de seguimiento a referencias del controlador LQ convencional. El mecanismo adaptativo se formula analizando cada elemento de la senal de control LQ-FF en relación con la regulación de estados, el cambio de referencia y la compensacion de perturbaciones. Además, el rechazo de perturbaciones se basa en los controladores Proporcional-Integral-Derivativo y el análisis teórico para controladores predictivos, los cuales tienen como objetivo obtener la dinámica inversa de las perturbaciones y las entradas del proceso. Se presenta una comparativa entre un modelo de espacio de estados aumentado y un modelo con aproximación de retardo polinomial para el tratamiento de los retardos asociados a las perturbaciones y las entradas del proceso en la formulacion del controlador. El método propuesto demuestra su eficacia en el control de un sistema de temperatura no lineal validado, manteniendo el rendimiento similar al controlador LQ convencional en el seguimiento de referencias y rechazando por completo los efectos de las perturbaciones. Para el escenario de simulacion presentado, la sintonía propuesta logra un 10 % menos de error de salida, con un incremento de solo un 18 % en el esfuerzo de control en comparacion con la sintonía convencional.

In this manuscript, we formulate and experimentally verify four state-of-the-art controlstrategies on Baxter, a 7-DOF redundant robot manipulator. The control strategies examined in this manuscript are the subject of active research in the field of non-linear control, and have the potential to significantly improve the performance of robot manipulators when they operate in unstructured environments. The first control strategy we investigate in this manuscript is model-free decentralized-adaptive control. The purpose of this control strategy is to achieve consistent performance across a wide range of joint configurations and end-effector inertias, while having a similar computational efficiency as PID approaches. The second control strategy we investigate in this manuscript is delay-adaptive control. The purpose of this control strategy is to simultaneously estimate and compensate for an unknown long actuator delay. The third control strategy we investigate in this manuscript is prescribed-time control. A key feature of this control strategy is that the settling time is explicitly assigned by the control designer to a value desired, or “prescribed” by the user, and that the settling time is independent of the initial conditions and of the reference signal. The fourth control strategy we investigate in this manuscript is the prescribed-time safety filter. This formation yields a filter that is capable of avoiding multiple obstacles in a minimally invasive manner with bounded joint torques, while simultaneously allowing a nominal controller to converge to positions located on the boundary of the safe set by the end of a fixed-duration task. Through the formulation and experimental verification of each control strategy we present in this manuscript, we demonstrate that our proposed methods perform well in both theory and in practice.

The ubiquity of dynamical systems in society has brought the subject matter of their safety to the fore. From small personal drones to autonomous vehicles and jumbo jets, the safety of dynamical systems has become critical and of utmost importance. In this dissertation, we develop control strategies for enforcing safety — characterized by state constraints — in nonlinear dynamical systems of two kinds. First, systems with input delays are considered. This class of systems is particularly relevant because delays abound in engineering applications and their effect can be catastrophic if not systematically addressed. We develop control strategies for enforcing safety in (i) systems with a single, time-varying input delay across all input channels, and (ii) systems with distinct, constant input delays across input channels. The control strategies developed utilize a nontrivial combination of state-predictors with a safe feedback law designed for the corresponding delay- free system. In the case of systems with distinct input delays, we introduce algorithms that enforce safety using a subset of shorter-delayed input channels whenever possible, allowing safety guarantees to be made before longer input delays have been compensated. This is a feature that is especially beneficial when input delays are of significantly different lengths. Next, a prescribed-time safety (PTSf) algorithm is developed for systems where safety is required for a finite, a priori prescribed time. In contrast to existing algorithms that only permit an asymptotic approach to (but not arrival at) the boundary of a safe set, PTSf allows a system to reach the boundary of a safe set — at an infinitely soft rate — at the end of the prescribed time, irrespective of initial condition. This feature is of interest in systems where the desired nominal behavior is prescribed-time stabilization to a set point on the boundary of the safe set. In addition to enforcing safety only for a prescribed time, PTSf is dev

The ubiquity of dynamical systems in society has brought the subject matter of their safety to the fore. From small personal drones to autonomous vehicles and jumbo jets, the safety of dynamical systems has become critical and of utmost importance. In this dissertation, we develop control strategies for enforcing safety — characterized by state constraints — in nonlinear dynamical systems of two kinds. First, systems with input delays are considered. This class of systems is particularly relevant because delays abound in engineering applications and their effect can be catastrophic if not systematically addressed. We develop control strategies for enforcing safety in (i) systems with a single, time-varying input delay across all input channels, and (ii) systems with distinct, constant input delays across input channels. The control strategies developed utilize a nontrivial combination of state-predictors with a safe feedback law designed for the corresponding delay- free system. In the case of systems with distinct input delays, we introduce algorithms that enforce safety using a subset of shorter-delayed input channels whenever possible, allowing safety guarantees to be made before longer input delays have been compensated. This is a feature that is especially beneficial when input delays are of significantly different lengths. Next, a prescribed-time safety (PTSf) algorithm is developed for systems where safety is required for a finite, a priori prescribed time. In contrast to existing algorithms that only permit an asymptotic approach to (but not arrival at) the boundary of a safe set, PTSf allows a system to reach the boundary of a safe set — at an infinitely soft rate — at the end of the prescribed time, irrespective of initial condition. This feature is of interest in systems where the desired nominal behavior is prescribed-time stabilization to a set point on the boundary of the safe set. In addition to enforcing safety only for a prescribed time, PTSf is dev

In this manuscript, we formulate and experimentally verify four state-of-the-art controlstrategies on Baxter, a 7-DOF redundant robot manipulator. The control strategies examined in this manuscript are the subject of active research in the field of non-linear control, and have the potential to significantly improve the performance of robot manipulators when they operate in unstructured environments. The first control strategy we investigate in this manuscript is model-free decentralized-adaptive control. The purpose of this control strategy is to achieve consistent performance across a wide range of joint configurations and end-effector inertias, while having a similar computational efficiency as PID approaches. The second control strategy we investigate in this manuscript is delay-adaptive control. The purpose of this control strategy is to simultaneously estimate and compensate for an unknown long actuator delay. The third control strategy we investigate in this manuscript is prescribed-time control. A key feature of this control strategy is that the settling time is explicitly assigned by the control designer to a value desired, or “prescribed” by the user, and that the settling time is independent of the initial conditions and of the reference signal. The fourth control strategy we investigate in this manuscript is the prescribed-time safety filter. This formation yields a filter that is capable of avoiding multiple obstacles in a minimally invasive manner with bounded joint torques, while simultaneously allowing a nominal controller to converge to positions located on the boundary of the safe set by the end of a fixed-duration task. Through the formulation and experimental verification of each control strategy we present in this manuscript, we demonstrate that our proposed methods perform well in both theory and in practice.

This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameterize the delay in terms of piecewise-quadratic basis functions, thus yielding a finite-dimensional approximate problem with continuous-time inequality constraints induced by the delay bounds. We then exploit the quadratic structure of the delay to convert these continuous-time constraints into a finite set of canonical point constraints. We also develop an efficient numerical method for computing the gradients of the system cost function. This method, which involves integrating an auxiliary impulsive system with time-varying advance backwards in time, can be combined with any existing gradient-based optimization algorithm to generate approximate solutions for the optimal control problem.

Tracking of a desired pressure profile is key in mechanical ventilation to sufficiently support a patient. The aim of this paper is to improve pressure tracking performance of mechanical ventilation systems. This is achieved by explicitly taking into account the nonlinear hose characteristics and delays in the control strategy. Through an experimental case study it is shown that this can significantly improve tracking performance.

Tracking of a desired pressure profile is key in mechanical ventilation to sufficiently support a patient. The aim of this paper is to improve pressure tracking performance of mechanical ventilation systems. This is achieved by explicitly taking into account the nonlinear hose characteristics and delays in the control strategy. Through an experimental case study it is shown that this can significantly improve tracking performance.

This paper presents a detailed experimental comparison of control architectures for delayed bilateral teleoperation. The main goal is to illustrate the key differences in controller performance that can be expected in practice, independent of the human operator, as a function of the communication delay. Existing architectures can be divided into bilateral motion synchronization, where the master and slave controllers implement an as-stiff-as-possible coupling between the master and slave devices, and direct force-reflecting architectures, where the slave controller mimics the operator action, and the master controller reflects the slave-environment interaction forces. Six architectures are analyzed using standard performance indices to assess motion tracking, force reflection, and stiffness reflection quality. In addition, the architectures are also compared on physical operator effort, which is a newly introduced metric to quantify the required operator's effort to execute free motion tasks. The results illustrate that, for increasing delays, direct force-reflecting architectures (in particular, a position/force-force architecture) are superior to bilateral motion synchronizing controllers, in the sense that they are the least sensitive to delays. In contrast, all bilateral motion synchronizing architectures significantly suffer from a reduction in motion tracking or stiffness reflection, or an increased operator effort, when the delay increases. While these conclusions are drawn on a one-degree-of-freedom (DOF) setup, we expect these trends to maintain valid in general, and therefore, the authors suggest that future controller designs for delayed bilateral teleoperation should explore direct force-reflecting architectures more extensively to achieve better performance.

This paper presents a detailed experimental comparison of control architectures for delayed bilateral teleoperation. The main goal is to illustrate the key differences in controller performance that can be expected in practice, independent of the human operator, as a function of the communication delay. Existing architectures can be divided into bilateral motion synchronization, where the master and slave controllers implement an as-stiff-as-possible coupling between the master and slave devices, and direct force-reflecting architectures, where the slave controller mimics the operator action, and the master controller reflects the slave-environment interaction forces. Six architectures are analyzed using standard performance indices to assess motion tracking, force reflection, and stiffness reflection quality. In addition, the architectures are also compared on physical operator effort, which is a newly introduced metric to quantify the required operator's effort to execute free motion tasks. The results illustrate that, for increasing delays, direct force-reflecting architectures (in particular, a position/force-force architecture) are superior to bilateral motion synchronizing controllers, in the sense that they are the least sensitive to delays. In contrast, all bilateral motion synchronizing architectures significantly suffer from a reduction in motion tracking or stiffness reflection, or an increased operator effort, when the delay increases. While these conclusions are drawn on a one-degree-of-freedom (DOF) setup, we expect these trends to maintain valid in general, and therefore, the authors suggest that future controller designs for delayed bilateral teleoperation should explore direct force-reflecting architectures more extensively to achieve better performance.

Physical dynamical systems are able to process information in a nontrivial manner. In this thesis we evaluate the information processing capacity (IPC) in an experimental setup to assess information processing in a reservoir computer that consists of an analog Mackey-Glass nonlinearity coupled to itself via a delay line. We link the different dynamical regimes of this system to distinct modes of information processing and assess the influence of various dynamical phenomena, such as fixed point, periodic and chaotic dynamics on computation carried out by the system. We measure nonlinear memory up to seventh order and give its distribution as a function of the system parameters. Further we explore the influence of noise by performing matching numerical simulations. Thereby we find that the presence of noise, which is inevitable in every experimental setup, does not homogeneously degrade a system's computational power as measured by the IPC, but instead implies a change in the distribution of capacity across the degrees of information processing observed in the system. Finally, we use theoretical considerations from the literature on the IPC to explain our observations and distill suggestions to guide experimental setup.

In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and the control station is an often-present issue which compromises control performance and may even cause instability. A very relevant scenario in which network-induced delay needs to be investigated is costly usage of communication resources. More precisely, advanced communication technologies, e.g., 5G, are capable of offering latency-varying information exchange for different prices. Therefore, induced delay becomes a decision variable. It is then the matter of decision maker's willingness to either pay the required cost to have low-latency access to the communication resource, or delay the access at a reduced price. In this letter, we consider optimal price-based bi-variable decision making problem for single-loop NCS with a stochastic linear time-invariant system. Assuming that communication incurs cost such that transmission with shorter delay is more costly, a decision maker determines the switching strategy between communication links of different delays such that an optimal balance between the control performance and the communication cost is maintained. In this letter, we show that, under mild assumptions on the available information for decision makers, the separation property holds between the optimal link selecting and control policies. As the cost function is decomposable, the optimal policies are efficiently computed. © 2017 IEEE., QC 20200903

The robot manipulators are used in network-based industrial units, and even homes, by expending a significant lumped amount of energy. Manipulators are also subject to large time delays like many engineering systems, which may lead to the lack of high precision required and could cause not only poor control performance, but also catastrophic instability. Hence designing control algorithms for such delay systems to compensate for the time delay and having a robust control law is a necessity. Another important point which needs to be noticed in utilizing robots is environmental uncertainties, which may not be considered in the modeling. To summarize, parametric uncertainty and/or time-delay through manipulation along with optimal operation are important criteria for the operation of robotic systems. One of the main contributions of this dissertation is focusing on the development of robust techniques for achieving optimal operation and control of the arm to attain perfect tracking. For the operational optimization, we examine a discrete-time multi-variable gradient-based Extremum Seeking (ES) scheme enforcing operational time and torque saturation constraints to minimize the lumped amount of energy consumed for a path given. Finally, the optimal trajectory is experimentally implemented to be thoroughly compared with the inefficient one. Precise control of manipulators in the presence of delay or uncertainty and variation in their environments is also a prerequisite to feasibly utilize robot manipulators. Nonlinear control theorems for nonlinear systems (e.g. robotic systems) have been developed for a long period, however, implementing them, in reality, is one of the most challenging problems in engineering applications. Therefore, formulating novel robust and computationally efficient control approaches is still a necessity. Another significant contribution of this work is a practical implementation of various control theories, with verifying all the necessary assumpt

The paper deals with a two-person zero-sum differential game for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional of this game, we derive the Hamilton-Jacobi type equation with coinvariant derivatives. It is proved that, if the solution of this equation satisfies certain smoothness conditions, then it coincides with the value functional. On the other hand, it is proved that, at the points of coinvariant differentiability, the value functional satisfies the derived Hamilton-Jacobi equation. Therefore, this equation can be called the Hamilton-Jacobi-Bellman-Isaacs equation for time-delay systems. © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

The robot manipulators are used in network-based industrial units, and even homes, by expending a significant lumped amount of energy. Manipulators are also subject to large time delays like many engineering systems, which may lead to the lack of high precision required and could cause not only poor control performance, but also catastrophic instability. Hence designing control algorithms for such delay systems to compensate for the time delay and having a robust control law is a necessity. Another important point which needs to be noticed in utilizing robots is environmental uncertainties, which may not be considered in the modeling. To summarize, parametric uncertainty and/or time-delay through manipulation along with optimal operation are important criteria for the operation of robotic systems. One of the main contributions of this dissertation is focusing on the development of robust techniques for achieving optimal operation and control of the arm to attain perfect tracking. For the operational optimization, we examine a discrete-time multi-variable gradient-based Extremum Seeking (ES) scheme enforcing operational time and torque saturation constraints to minimize the lumped amount of energy consumed for a path given. Finally, the optimal trajectory is experimentally implemented to be thoroughly compared with the inefficient one. Precise control of manipulators in the presence of delay or uncertainty and variation in their environments is also a prerequisite to feasibly utilize robot manipulators. Nonlinear control theorems for nonlinear systems (e.g. robotic systems) have been developed for a long period, however, implementing them, in reality, is one of the most challenging problems in engineering applications. Therefore, formulating novel robust and computationally efficient control approaches is still a necessity. Another significant contribution of this work is a practical implementation of various control theories, with verifying all the necessary assumpt

Consistency is a powerful concept to characterize and classify the behavior of driven dynamical systems, therefore playing an essential role for the understanding of information processing in and by complex photonic systems. Here, we discuss two different experimental configurations of semiconductor laser systems with delayed optical feedback allowing for a unifying view via the detailed characterization and comparison of consistency and synchronization properties. The first configuration comprises two unidirectionally coupled semiconductor lasers, which has found considerable interest for applications in encrypted communication. The second configuration consists of a single laser with two optical delay loops of significantly different lengths, designed such that only one loop is active at a time and that allows to study replays of injected optical signals. We show that, in terms of three characteristic correlation measures-consistency correlation, transformation correlation, and spurious correlation-the dynamical features of the two different experiments are very similar and how the two configurations are connected. Our approach shows that consistency allows to understand and relate various chaos synchronization and stability properties. We particularly discuss the experimental results in the context of a previously established analytical framework, providing a common dynamical interpretation of consistency and chaos synchronization in delay-driven laser systems.

This paper introduces an explicit reference governor to supervise closed-loop linear time-delay systems. The proposed scheme enforces state and input constraints by modifying the reference of the supervised system so that the state vector always belongs to admissible sublevel sets of a suitably defined Lyapunov-Krasovskii functional. To accomplish this, this paper extends the existing definition of 'dynamic safety margin' to a time-delay setting and illustrates how to employ classic Lyapunov-Krasovskii functionals even though the reference is time varying. Constraint enforcement for arbitrary reference signals and asymptotic convergence to any strictly steady-state admissible set point is rigorously proven. Experimental results are reported to demonstrate the simplicity, practicality, and robustness of the proposed method., SCOPUS: ar.j, info:eu-repo/semantics/published

This thesis, which mainly consists of six appended papers, primarily considers a number of inverse problems in imaging and system identification. In particular, the first two papers generalize results for the rational covariance extension problem from one to higher dimensions. The rational covariance extension problem stems from system identification and can be formulated as a trigonometric moment problem, but with a complexity constraint on the sought measure. The papers investigate a solution method based on varia tional regularization and convex optimization. We prove the existence and uniqueness of a solution to the variational problem, both when enforcing exact moment matching and when considering two different versions of approximate moment matching. A number of related questions are also considered, such as well-posedness, and the theory is illustrated with a number of examples. The third paper considers the maximum delay margin problem in robust control: To find the largest time delay in a feedback loop for a linear dynamical system so that there still exists a single controller that stabilizes the system for all delays smaller than or equal to this time delay. A sufficient condition for robust stabilization is recast as an analytic interpolation problem, which leads to an algorithm for computing a lower bound on the maximum delay margin. The algorithm is based on bisection, where positive semi-definiteness of a Pick matrix is used as selection criteria. Paper four investigate the use of optimal transport as a regularizing functional to incorporate prior information in variational formulations for image reconstruction. This is done by observing that the so-called Sinkhorn iterations, which are used to solve large scale optimal transport problems, can be seen as coordinate ascent in a dual optimization problem. Using this, we extend the idea of Sinkhorn iterations and derive a iterative algorithm for computing the proximal operator. This allows us to solve la, Denna avhandling, som huvudsakligen består av de sex bifogade artiklarna, berör ett antal olika inversa problem med tillämpning inom bildrekonstruktion och systemidentifiering. The två första artiklarna generaliserar resultat från litteraturen gällande det rationella kovariansutvidgningsproblemet, från det en-dimensionella fallet till det fler-dimensionella fallet. Det rationella kovariansutvidgningsproblemet har sitt ursprung inom systemidentifiering och kan formuleras som ett trigonometriska momentproblem. Momentproblemet är dock av icke-klassisk karaktär, eftersom det sökta måttet har ett bivillkor som begränsar dess komplexitet. Papperna undersöker olika metoder för att lösa problemet, metoder som alla bygger på variationell regularisering och konvex optimering. Vi undersöker både exakt och approximativ kovariansmatchning, och huvudresultaten är bevis av existens och unikhet vad gäller lösning till dessa olika problem. Artiklarna undersöker även ett antal relaterade frågor, så som välställdhet av problemen, och teorin är också illustrerad med ett antal olika exempel och tillämpningar. Det tredje pappret behandlar ett problem inom robust reglering för linjära system: ett systems tidsfördröjningsmarginal. Tidsfördröjningsmarginalen är den längsta tidsfördröjning ett återkopplat linjärt dynamiskt system kan ha så att det fortfarande finns en enda regulator som stabiliserar systemet för alla tidsfördröjningar som är kortare. Artikeln undersöker ett tillräckligt villkor, och formulerar om detta som ett analytiskt interpolationsproblem. Detta leder till en algoritm för att beräkna en undre gräns för tidsfördröjningsmarginalen. Algoritmen bygger på intervallhalveringsmetoden, och använder Pick-matrisens teckenkaraktär som urvalskriterium. Artikel fyra undersöker användandet av optimal masstransport som regulariseringsfunktion vid bildrekonstruktion. Idén är att använda optimal masstransport som ett avstånd mellan bilder, och på så vis kunna inkorporera förhandsinformat, QC 20181204

We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies the existence of a max-separable Lyapunov function on a compact set; second, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and insensitivity to time delays. This paper establishes that for monotone nonlinear systems, equivalence holds between asymptotic stability, the existence of a max-separable Lyapunov function, D-stability, and insensitivity to bounded and unbounded time-varying delays. In particular, a new and general notion of D-stability for monotone nonlinear systems is discussed, and a set of necessary and sufficient conditions for delay-independent stability are derived. Examples show how the results extend the state of the art., QC 20180403

This thesis, which mainly consists of six appended papers, primarily considers a number of inverse problems in imaging and system identification. In particular, the first two papers generalize results for the rational covariance extension problem from one to higher dimensions. The rational covariance extension problem stems from system identification and can be formulated as a trigonometric moment problem, but with a complexity constraint on the sought measure. The papers investigate a solution method based on varia tional regularization and convex optimization. We prove the existence and uniqueness of a solution to the variational problem, both when enforcing exact moment matching and when considering two different versions of approximate moment matching. A number of related questions are also considered, such as well-posedness, and the theory is illustrated with a number of examples. The third paper considers the maximum delay margin problem in robust control: To find the largest time delay in a feedback loop for a linear dynamical system so that there still exists a single controller that stabilizes the system for all delays smaller than or equal to this time delay. A sufficient condition for robust stabilization is recast as an analytic interpolation problem, which leads to an algorithm for computing a lower bound on the maximum delay margin. The algorithm is based on bisection, where positive semi-definiteness of a Pick matrix is used as selection criteria. Paper four investigate the use of optimal transport as a regularizing functional to incorporate prior information in variational formulations for image reconstruction. This is done by observing that the so-called Sinkhorn iterations, which are used to solve large scale optimal transport problems, can be seen as coordinate ascent in a dual optimization problem. Using this, we extend the idea of Sinkhorn iterations and derive a iterative algorithm for computing the proximal operator. This allows us to solve la, Denna avhandling, som huvudsakligen består av de sex bifogade artiklarna, berör ett antal olika inversa problem med tillämpning inom bildrekonstruktion och systemidentifiering. The två första artiklarna generaliserar resultat från litteraturen gällande det rationella kovariansutvidgningsproblemet, från det en-dimensionella fallet till det fler-dimensionella fallet. Det rationella kovariansutvidgningsproblemet har sitt ursprung inom systemidentifiering och kan formuleras som ett trigonometriska momentproblem. Momentproblemet är dock av icke-klassisk karaktär, eftersom det sökta måttet har ett bivillkor som begränsar dess komplexitet. Papperna undersöker olika metoder för att lösa problemet, metoder som alla bygger på variationell regularisering och konvex optimering. Vi undersöker både exakt och approximativ kovariansmatchning, och huvudresultaten är bevis av existens och unikhet vad gäller lösning till dessa olika problem. Artiklarna undersöker även ett antal relaterade frågor, så som välställdhet av problemen, och teorin är också illustrerad med ett antal olika exempel och tillämpningar. Det tredje pappret behandlar ett problem inom robust reglering för linjära system: ett systems tidsfördröjningsmarginal. Tidsfördröjningsmarginalen är den längsta tidsfördröjning ett återkopplat linjärt dynamiskt system kan ha så att det fortfarande finns en enda regulator som stabiliserar systemet för alla tidsfördröjningar som är kortare. Artikeln undersöker ett tillräckligt villkor, och formulerar om detta som ett analytiskt interpolationsproblem. Detta leder till en algoritm för att beräkna en undre gräns för tidsfördröjningsmarginalen. Algoritmen bygger på intervallhalveringsmetoden, och använder Pick-matrisens teckenkaraktär som urvalskriterium. Artikel fyra undersöker användandet av optimal masstransport som regulariseringsfunktion vid bildrekonstruktion. Idén är att använda optimal masstransport som ett avstånd mellan bilder, och på så vis kunna inkorporera förhandsinformat, QC 20181204

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.

This thesis, which mainly consists of six appended papers, primarily considers a number of inverse problems in imaging and system identification. In particular, the first two papers generalize results for the rational covariance extension problem from one to higher dimensions. The rational covariance extension problem stems from system identification and can be formulated as a trigonometric moment problem, but with a complexity constraint on the sought measure. The papers investigate a solution method based on varia tional regularization and convex optimization. We prove the existence and uniqueness of a solution to the variational problem, both when enforcing exact moment matching and when considering two different versions of approximate moment matching. A number of related questions are also considered, such as well-posedness, and the theory is illustrated with a number of examples. The third paper considers the maximum delay margin problem in robust control: To find the largest time delay in a feedback loop for a linear dynamical system so that there still exists a single controller that stabilizes the system for all delays smaller than or equal to this time delay. A sufficient condition for robust stabilization is recast as an analytic interpolation problem, which leads to an algorithm for computing a lower bound on the maximum delay margin. The algorithm is based on bisection, where positive semi-definiteness of a Pick matrix is used as selection criteria. Paper four investigate the use of optimal transport as a regularizing functional to incorporate prior information in variational formulations for image reconstruction. This is done by observing that the so-called Sinkhorn iterations, which are used to solve large scale optimal transport problems, can be seen as coordinate ascent in a dual optimization problem. Using this, we extend the idea of Sinkhorn iterations and derive a iterative algorithm for computing the proximal operator. This allows us to solve la, Denna avhandling, som huvudsakligen består av de sex bifogade artiklarna, berör ett antal olika inversa problem med tillämpning inom bildrekonstruktion och systemidentifiering. The två första artiklarna generaliserar resultat från litteraturen gällande det rationella kovariansutvidgningsproblemet, från det en-dimensionella fallet till det fler-dimensionella fallet. Det rationella kovariansutvidgningsproblemet har sitt ursprung inom systemidentifiering och kan formuleras som ett trigonometriska momentproblem. Momentproblemet är dock av icke-klassisk karaktär, eftersom det sökta måttet har ett bivillkor som begränsar dess komplexitet. Papperna undersöker olika metoder för att lösa problemet, metoder som alla bygger på variationell regularisering och konvex optimering. Vi undersöker både exakt och approximativ kovariansmatchning, och huvudresultaten är bevis av existens och unikhet vad gäller lösning till dessa olika problem. Artiklarna undersöker även ett antal relaterade frågor, så som välställdhet av problemen, och teorin är också illustrerad med ett antal olika exempel och tillämpningar. Det tredje pappret behandlar ett problem inom robust reglering för linjära system: ett systems tidsfördröjningsmarginal. Tidsfördröjningsmarginalen är den längsta tidsfördröjning ett återkopplat linjärt dynamiskt system kan ha så att det fortfarande finns en enda regulator som stabiliserar systemet för alla tidsfördröjningar som är kortare. Artikeln undersöker ett tillräckligt villkor, och formulerar om detta som ett analytiskt interpolationsproblem. Detta leder till en algoritm för att beräkna en undre gräns för tidsfördröjningsmarginalen. Algoritmen bygger på intervallhalveringsmetoden, och använder Pick-matrisens teckenkaraktär som urvalskriterium. Artikel fyra undersöker användandet av optimal masstransport som regulariseringsfunktion vid bildrekonstruktion. Idén är att använda optimal masstransport som ett avstånd mellan bilder, och på så vis kunna inkorporera förhandsinformat, QC 20181204

This thesis, which mainly consists of six appended papers, primarily considers a number of inverse problems in imaging and system identification. In particular, the first two papers generalize results for the rational covariance extension problem from one to higher dimensions. The rational covariance extension problem stems from system identification and can be formulated as a trigonometric moment problem, but with a complexity constraint on the sought measure. The papers investigate a solution method based on varia tional regularization and convex optimization. We prove the existence and uniqueness of a solution to the variational problem, both when enforcing exact moment matching and when considering two different versions of approximate moment matching. A number of related questions are also considered, such as well-posedness, and the theory is illustrated with a number of examples. The third paper considers the maximum delay margin problem in robust control: To find the largest time delay in a feedback loop for a linear dynamical system so that there still exists a single controller that stabilizes the system for all delays smaller than or equal to this time delay. A sufficient condition for robust stabilization is recast as an analytic interpolation problem, which leads to an algorithm for computing a lower bound on the maximum delay margin. The algorithm is based on bisection, where positive semi-definiteness of a Pick matrix is used as selection criteria. Paper four investigate the use of optimal transport as a regularizing functional to incorporate prior information in variational formulations for image reconstruction. This is done by observing that the so-called Sinkhorn iterations, which are used to solve large scale optimal transport problems, can be seen as coordinate ascent in a dual optimization problem. Using this, we extend the idea of Sinkhorn iterations and derive a iterative algorithm for computing the proximal operator. This allows us to solve la, Denna avhandling, som huvudsakligen består av de sex bifogade artiklarna, berör ett antal olika inversa problem med tillämpning inom bildrekonstruktion och systemidentifiering. The två första artiklarna generaliserar resultat från litteraturen gällande det rationella kovariansutvidgningsproblemet, från det en-dimensionella fallet till det fler-dimensionella fallet. Det rationella kovariansutvidgningsproblemet har sitt ursprung inom systemidentifiering och kan formuleras som ett trigonometriska momentproblem. Momentproblemet är dock av icke-klassisk karaktär, eftersom det sökta måttet har ett bivillkor som begränsar dess komplexitet. Papperna undersöker olika metoder för att lösa problemet, metoder som alla bygger på variationell regularisering och konvex optimering. Vi undersöker både exakt och approximativ kovariansmatchning, och huvudresultaten är bevis av existens och unikhet vad gäller lösning till dessa olika problem. Artiklarna undersöker även ett antal relaterade frågor, så som välställdhet av problemen, och teorin är också illustrerad med ett antal olika exempel och tillämpningar. Det tredje pappret behandlar ett problem inom robust reglering för linjära system: ett systems tidsfördröjningsmarginal. Tidsfördröjningsmarginalen är den längsta tidsfördröjning ett återkopplat linjärt dynamiskt system kan ha så att det fortfarande finns en enda regulator som stabiliserar systemet för alla tidsfördröjningar som är kortare. Artikeln undersöker ett tillräckligt villkor, och formulerar om detta som ett analytiskt interpolationsproblem. Detta leder till en algoritm för att beräkna en undre gräns för tidsfördröjningsmarginalen. Algoritmen bygger på intervallhalveringsmetoden, och använder Pick-matrisens teckenkaraktär som urvalskriterium. Artikel fyra undersöker användandet av optimal masstransport som regulariseringsfunktion vid bildrekonstruktion. Idén är att använda optimal masstransport som ett avstånd mellan bilder, och på så vis kunna inkorporera förhandsinformat, QC 20181204

This thesis, which mainly consists of six appended papers, primarily considers a number of inverse problems in imaging and system identification. In particular, the first two papers generalize results for the rational covariance extension problem from one to higher dimensions. The rational covariance extension problem stems from system identification and can be formulated as a trigonometric moment problem, but with a complexity constraint on the sought measure. The papers investigate a solution method based on varia tional regularization and convex optimization. We prove the existence and uniqueness of a solution to the variational problem, both when enforcing exact moment matching and when considering two different versions of approximate moment matching. A number of related questions are also considered, such as well-posedness, and the theory is illustrated with a number of examples. The third paper considers the maximum delay margin problem in robust control: To find the largest time delay in a feedback loop for a linear dynamical system so that there still exists a single controller that stabilizes the system for all delays smaller than or equal to this time delay. A sufficient condition for robust stabilization is recast as an analytic interpolation problem, which leads to an algorithm for computing a lower bound on the maximum delay margin. The algorithm is based on bisection, where positive semi-definiteness of a Pick matrix is used as selection criteria. Paper four investigate the use of optimal transport as a regularizing functional to incorporate prior information in variational formulations for image reconstruction. This is done by observing that the so-called Sinkhorn iterations, which are used to solve large scale optimal transport problems, can be seen as coordinate ascent in a dual optimization problem. Using this, we extend the idea of Sinkhorn iterations and derive a iterative algorithm for computing the proximal operator. This allows us to solve la, Denna avhandling, som huvudsakligen består av de sex bifogade artiklarna, berör ett antal olika inversa problem med tillämpning inom bildrekonstruktion och systemidentifiering. The två första artiklarna generaliserar resultat från litteraturen gällande det rationella kovariansutvidgningsproblemet, från det en-dimensionella fallet till det fler-dimensionella fallet. Det rationella kovariansutvidgningsproblemet har sitt ursprung inom systemidentifiering och kan formuleras som ett trigonometriska momentproblem. Momentproblemet är dock av icke-klassisk karaktär, eftersom det sökta måttet har ett bivillkor som begränsar dess komplexitet. Papperna undersöker olika metoder för att lösa problemet, metoder som alla bygger på variationell regularisering och konvex optimering. Vi undersöker både exakt och approximativ kovariansmatchning, och huvudresultaten är bevis av existens och unikhet vad gäller lösning till dessa olika problem. Artiklarna undersöker även ett antal relaterade frågor, så som välställdhet av problemen, och teorin är också illustrerad med ett antal olika exempel och tillämpningar. Det tredje pappret behandlar ett problem inom robust reglering för linjära system: ett systems tidsfördröjningsmarginal. Tidsfördröjningsmarginalen är den längsta tidsfördröjning ett återkopplat linjärt dynamiskt system kan ha så att det fortfarande finns en enda regulator som stabiliserar systemet för alla tidsfördröjningar som är kortare. Artikeln undersöker ett tillräckligt villkor, och formulerar om detta som ett analytiskt interpolationsproblem. Detta leder till en algoritm för att beräkna en undre gräns för tidsfördröjningsmarginalen. Algoritmen bygger på intervallhalveringsmetoden, och använder Pick-matrisens teckenkaraktär som urvalskriterium. Artikel fyra undersöker användandet av optimal masstransport som regulariseringsfunktion vid bildrekonstruktion. Idén är att använda optimal masstransport som ett avstånd mellan bilder, och på så vis kunna inkorporera förhandsinformat, QC 20181204

We present stability criteria for equilibria of a class of linear complementarity systems, subjected to discrete and distributed delay. We present necessary and sufficient conditions for local exponential stability, inferred from the spectrum location of a corresponding system of delay differential algebraic equations. Subsequently, we obtain sufficient LMI-based conditions for global asymptotic stability using Lyapunov–Krasovskii functionals.

We present stability criteria for equilibria of a class of linear complementarity systems, subjected to discrete and distributed delay. We present necessary and sufficient conditions for local exponential stability, inferred from the spectrum location of a corresponding system of delay differential algebraic equations. Subsequently, we obtain sufficient LMI-based conditions for global asymptotic stability using Lyapunov–Krasovskii functionals.

This paper presents a procedure to transform a chaotic logistic map into a continuous-time delay chaotic system by using sampled-data representation of continuous-time models. Because of this, the chaotic behavior of the resultant scheme is easy to proofread. A numerical illustration is also realized by utilizing Matlab/Simulink, where the new resultant chaotic attractor is shown, Postprint (published version)

In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process., QC 20160615

The paper is focused on systems with delay terms at the left (and the right) side of differential equations. Analysis and synthesis of delay systems can be conveniently studied through a special ring of RQ-meromorphic functions. The control methodology is based on a solution of Diophantine equations in this ring. Final controllers result in the Smith predictor like structure. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. The methodology is illustrated by a stable second order transfer function with a dead-time term. Then the paper brings an autotuning method as a combination of biased-relay feedback estimation and the proposed algebraic control design. The developed approach is illustrated by examples in the Matlab and Simulink environment. © 2016 IEEE.

The paper is focused on systems with delay terms at the left (and the right) side of differential equations. Analysis and synthesis of delay systems can be conveniently studied through a special ring of RQ-meromorphic functions. The control methodology is based on a solution of Diophantine equations in this ring. Final controllers result in the Smith predictor like structure. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. The methodology is illustrated by a stable second order transfer function with a dead-time term. Then the paper brings an autotuning method as a combination of biased-relay feedback estimation and the proposed algebraic control design. The developed approach is illustrated by examples in the Matlab and Simulink environment. © 2016 IEEE.

It is shown that an impulsive system with a time-delay in the continuous part can be equivalently represented by discrete dynamics under less restrictive conditions on the time-delay value than considered previously.

We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is based on an extension of a delay-independent stability result for monotone systems under constant delays by Smith to systems with bounded heterogenous time-varying delays. Under the additional assumption of positivity and sub-homogenousvector fields, we establish the aforementioned delay insensitivity property and derive a novel test for global asymptotic stability. If the system has a unique equilibrium point in the positive orthant, we prove that our stability test is necessary and sufficient. Specialized to positive linear systems, our results extend and sharpen existing results from the literature., QC 20150327

The use of the ring of quasipolynomial meromorphic functions for algebraic control design for time delay systems in a robust sense is the aim of this paper. Unlike the habitual simple feedback loop, Two-Feedback-Controllers control system structure is intended to be utilized, which involves making some robust analysis first. Tunable controller parameters are set such that requirements of robust stability and robust performance are satisfied. The theoretically described methodology is verified by simulations in Matlab/Simulink environment followed by real experiments with temperature control of a laboratory circuit heating plant containing internal as well as input-output delays. The obtained results promise the applicability of the controller design approach. © 2014 IEEE.

The use of the ring of quasipolynomial meromorphic functions for algebraic control design for time delay systems in a robust sense is the aim of this paper. Unlike the habitual simple feedback loop, Two-Feedback-Controllers control system structure is intended to be utilized, which involves making some robust analysis first. Tunable controller parameters are set such that requirements of robust stability and robust performance are satisfied. The theoretically described methodology is verified by simulations in Matlab/Simulink environment followed by real experiments with temperature control of a laboratory circuit heating plant containing internal as well as input-output delays. The obtained results promise the applicability of the controller design approach. © 2014 IEEE.

We model the performance of an optoelectronic phase-chaos system operating with telecom components to generate random bits. The key component of the system is differential delay, namely the system is subject to two delay times which differ in an amount much larger than the autocorrelation time. This is implemented by a delay loop and an imbalanced Mach-Zhender modulator. We show that after suitable digitalization of the chaotic signal the generated bits pass all the NIST test for randomness. We also show that the system can be extended to have several chains in parallel each with a Mach-Zhender modulator, each chain being used to produce a sequence of random bits. If the differential delays of the Mach-Zhenders differ by an amount larger than the autocorrelation time of the chaotic dynamics, the output of the different chains is uncorrelated and therefore can be used for parallel generation of statistically independent random bit-streams. In addition, we also find that a sequence constructed by interleaving the parallel bit-streams also pass all the NIST tests for randomness. Based on the least significant bits which can be included in the sequence and the number of the parallel branches which can be implemented, we show that bit rates up to Tb/s can be achieved. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

An important issue in the trends of miniaturization of Systems on Chips (SoCs) is to obtain a high energy efficiency. This can be reached by Dynamic Voltage Scaling (DVS) architectures as the novel discrete Vdd-Hopping circuit. Generally, this kind of systems present parameter uncertainties and delays. Likewise, current peaks and energy dissipation must be reduced. In this paper, an optimal and robust saturated control law is proposed for this Vdd-Hopping circuit via Lyapunov-Krasovskii theory that ensures asymptotic stability as well as system robustness with respect to delay presence and parameter uncertainties. The closed-loop system presents a regional stabilization due to the actuator saturation. An estimation of an attraction domain is provided. This controller also limites the current peaks and it provides an energy-aware performance. The advantages achieved with this controller are shown in simulation.

In a wireless communication network, different users share a common resource. An objective of radio resource management is to assign the resources in an effective way among the users. Power control is an important component in this setting that has been extensively studied over the last two decades. In many real networks, there are inherent time delays due to filtering of signals and control signalling. Time delays can affect stability and convergence properties of the power control algorithms. We therefore consider power control laws of higher order to include models with delays and delay compensation. The main contribution of this paper is to exploit more structure of the interference feedback to prove less conservative conditions for system stability. Our primary tool to reduce conservativeness is to use scalings in an input-output framework for stability analysis., QC 20130520

An important issue in the trends of miniaturization of Systems on Chips (SoCs) is to obtain a high energy efficiency. This can be reached by Dynamic Voltage Scaling (DVS) architectures as the novel discrete Vdd-Hopping circuit. Generally, this kind of systems present parameter uncertainties and delays. Likewise, current peaks and energy dissipation must be reduced. In this paper, an optimal and robust saturated control law is proposed for this Vdd-Hopping circuit via Lyapunov-Krasovskii theory that ensures asymptotic stability as well as system robustness with respect to delay presence and parameter uncertainties. The closed-loop system presents a regional stabilization due to the actuator saturation. An estimation of an attraction domain is provided. This controller also limites the current peaks and it provides an energy-aware performance. The advantages achieved with this controller are shown in simulation.

An important issue in the trends of miniaturization of Systems on Chips (SoCs) is to obtain a high energy efficiency. This can be reached by Dynamic Voltage Scaling (DVS) architectures as the novel discrete Vdd-Hopping circuit. Generally, this kind of systems present parameter uncertainties and delays. Likewise, current peaks and energy dissipation must be reduced. In this paper, an optimal and robust saturated control law is proposed for this Vdd-Hopping circuit via Lyapunov-Krasovskii theory that ensures asymptotic stability as well as system robustness with respect to delay presence and parameter uncertainties. The closed-loop system presents a regional stabilization due to the actuator saturation. An estimation of an attraction domain is provided. This controller also limites the current peaks and it provides an energy-aware performance. The advantages achieved with this controller are shown in simulation.

An important issue in the trends of miniaturization of Systems on Chips (SoCs) is to obtain a high energy efficiency. This can be reached by Dynamic Voltage Scaling (DVS) architectures as the novel discrete Vdd-Hopping circuit. Generally, this kind of systems present parameter uncertainties and delays. Likewise, current peaks and energy dissipation must be reduced. In this paper, an optimal and robust saturated control law is proposed for this Vdd-Hopping circuit via Lyapunov-Krasovskii theory that ensures asymptotic stability as well as system robustness with respect to delay presence and parameter uncertainties. The closed-loop system presents a regional stabilization due to the actuator saturation. An estimation of an attraction domain is provided. This controller also limites the current peaks and it provides an energy-aware performance. The advantages achieved with this controller are shown in simulation.

The increasing amount of data being generated in different areas of science and technology require novel and efficient techniques of processing, going beyond traditional concepts. In this paper, we numerically study the information processing capabilities of semiconductor lasers subject to delayed optical feedback. Based on the recent concept of reservoir computing, we show that certain tasks, which are inherently hard for traditional computers, can be efficiently tackled by such systems. Major advantages of this approach comprise the possibility of simple and low-cost hardware implementation of the reservoir and ultrafast processing speed. Experimental results corroborate the numerical predictions. © 1995-2012 IEEE.

We investigate optimal boundary control of firstorder hyperbolic PDEs. These equations are ubiquitous in engineered systems, such as traffic flows, fluid flows, heat exchangers, chemical reactors, and oil production systems. We derive linear quadratic regulator (LQR) results using a weak variations approach, recently developed for parabolic PDEs. The distinguishing characteristic of this approach is that it provides a systematic procedure for deriving LQR control laws without semi-group theoretic concepts. Ultimately, these control laws are given by the solution of an associated Riccati PDE. We demonstrate the applicability of these results on two case studies: traffic flow control and input-delayed systems. Finally, we extend the LQR results to solve the output reference tracking problem. Unlike motion planning, these reference tracking equations do not require state trajectory generation.

We investigate optimal boundary control of firstorder hyperbolic PDEs. These equations are ubiquitous in engineered systems, such as traffic flows, fluid flows, heat exchangers, chemical reactors, and oil production systems. We derive linear quadratic regulator (LQR) results using a weak variations approach, recently developed for parabolic PDEs. The distinguishing characteristic of this approach is that it provides a systematic procedure for deriving LQR control laws without semi-group theoretic concepts. Ultimately, these control laws are given by the solution of an associated Riccati PDE. We demonstrate the applicability of these results on two case studies: traffic flow control and input-delayed systems. Finally, we extend the LQR results to solve the output reference tracking problem. Unlike motion planning, these reference tracking equations do not require state trajectory generation.