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This study presents the event-triggered control (ETC) for linear parameter varying (LPV) model of boost converters. We examine the nonlinear dynamics of boost converters in the LPV framework. The proposed controller is duty-ratio-dependent and provides better performance while requiring less computation. Using the parameter-dependent Lyapunov function (PDLF), we demonstrate the stablity analysis of the proposed approach. Furthermore, we demonstrate that the inter-event time is lower bound by a positive constant, which indicates Zeno behavior free performance. In comparison to earlier time-invariant synthesis techniques, the LPV formulation offers for increased robustness and performance properties. Simulation and experimental results validate the effectiveness of the proposed method.

We propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities (LMIs). We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever wellposedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunovbased designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.

International audience; Razumikhin-like theorems on hyperexponential and fixed-time stability of time-delay systems are proposed for both explicitly and implicitly defined Lyapunov functions. While the former method is useful for stability analysis, the latter approach is more suitable for control synthesis. Examples of systems that can be stabilized hyperexponentially and in fixed time are given. The control parameters tuning algorithm is presented in the form of linear matrix inequalities. The numerical simulations illustrate the theoretical results.

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part I. We present a necessary and sufficient LMI condition for the feasibility of a vector of power demands (under small perturbation), which extends a necessary condition in the literature. The alternatives of these LMI conditions are also included. In addition we refine these LMI conditions to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which allows for an alternative approach to determine power flow feasibility. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. Finally, we prove that the unique long-term voltage semi-stable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is obtained, as well as a parametrization of the boundary of the set of feasible power demands.

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part I. We present a necessary and sufficient LMI condition for the feasibility of a vector of power demands (under small perturbation), which extends a necessary condition in the literature. The alternatives of these LMI conditions are also included. In addition we refine these LMI conditions to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which allows for an alternative approach to determine power flow feasibility. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. Finally, we prove that the unique long-term voltage semi-stable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is obtained, as well as a parametrization of the boundary of the set of feasible power demands.

This paper proposes a data-driven model reduction approach on the basis of noisy data with a known noise model. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin projection to all systems explaining the data characterized in a large-dimensional quadratic matrix inequality (QMI) can again be characterized in a lower-dimensional QMI. Next, we develop a data-driven generalized balanced truncation method that relies on two steps. First, we provide necessary and sufficient conditions such that systems explaining the data have common generalized Gramians. Second, these common generalized Gramians are used to construct matrices that allow to characterize a class of reduced-order models via generalized balanced truncation in terms of a lower-dimensional QMI by applying the data reduction concept. Additionally, we present alternative procedures to compute a priori and a posteriori upper bounds with respect to the true system generating the data. Finally, the proposed techniques are illustrated by means of application to an example of a system of a cart with a double-pendulum.

International audience; The authors present a novel nonlinear Thau-Luenberger observer for estimating Structure from Motion using a calibrated camera. Accurate reconstruction of the 3D structure of a scene relies on precise estimation of the camera’s translational and angular velocities, which can be challenging for cameras on mobile platforms. The proposed observer aims to estimate these velocities robustly in the presence of measurement noise, with stability characterized through Input to State Stability analysis and Lyapunov theory. The stability conditions are determined using optimization techniques based on Linear Matrix Inequalities. The performance of the proposed approach is validated through simulation and experimental data, demonstrating its effectiveness in recovering the depth of tracked features and its robustness against disturbances.

In a recent paper, we have shown how to learn controllers for unknown linear systems using finite length noisy data by solving linear matrix inequalities. In this note, we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system.

Stable oscillations, arising from nonlinear non-equilibrium dynamics, are an important class of behavior in both nature and engineering. For engineering applications like robotic locomotion, it is usually desirable to induce oscillations in a controlled manner. While plenty of feedback control methods have been developed for equilibrium behaviors in control theory, we still lack a systematic design framework to excite non-oscillatory systems into oscillations via feedback control. As a step towards that, this thesis aims to provide theoretically guaranteed feedback controller design protocols for stable oscillations. Inspired by the oscillator models in biology and electrical engineering, we propose two architectures for oscillation control design: the mixed feedback oscillator and the resonant positive feedback oscillator. Our design methods take advantage of the dominant system theory to trigger and modulate stable oscillations in closed loop. For the mixed feedback oscillator, we show how to achieve oscillations by tuning the control parameters: the balance between the positive and negative feedback networks and the global feedback gain. For the resonant positive feedback oscillator, we show how to trigger oscillations by designing its linear and nonlinear control units. Then we show how to implement the two control architectures with basic linear and nonlinear circuit elements. Finally, we extend the control design for the mixed feedback oscillator. Based on linear matrix inequalities (LMIs) for dominance analysis, we develop control algorithms that automatically return state feedback gains that also take robustness and passivity-based interconnection into consideration.

This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the active mode is completely unknown and unobservable, and ii) the \emph{mode-dependent} case, in which the controller depends on the current active switching mode. The technical developments are based on graph-theory tools, relying in particular on the path-complete Lyapunov functions framework. The main idea is to use directed and labeled graphs to encode Lyapunov inequalities to design robust and mode-dependent piecewise linear state-feedback controllers. This results in novel and flexible conditions, with the particular feature of being in the form of linear matrix inequalities (LMIs). Our technique thus provides a first controller-design strategy allowing piecewise linear feedback maps and piecewise quadratic (control) Lyapunov functions by means of semidefinite programming. Numerical examples illustrate the application of the proposed techniques, the relations between the graph order, the robustness, and the performance of the closed loop.

This paper investigates the trajectory tracking control issue of four-wheel independently actuated electric vehicles (FWIA EVs) with steer-by-wire devices concerning parameter uncertainties, external disturbances, input saturation, and vehicle sideslip angle not easily obtained. A robustH∞dynamic output feedback control strategy is proposed for the integrated control of the steering motor current and direct yaw moment without using sideslip angle information to ensure the reference trajectory tracking and the improvement of handling performance and yaw stability. In the proposed integration control framework, the steer-by-wire device dynamic is involved in the polyhedral linear parameter-varying (LPV) trajectory tracking error model considering the time-varying longitudinal velocity, and the norm-bounded parameter uncertainties such as road adhesion coefficient, tire cornering stiffness, vehicle mass, and vehicle moment of inertia. With the help of the LPV model of all the states of the steer-by-wire FWIA EV, a dynamic output feedback trajectory tracking controller is designed using the robustH∞technique. The controller gain matrices are obtained by solving the linear matrix inequalities. Finally, the high-fidelity full-vehicle model based on the CarSim-MATLAB/Simulink joint simulation platform verifies the robustness and advantages of the designed control strategy in the accelerated lane-change scenario.

International audience; This paper addresses the problem of static output-feedback control design for uncertain discrete-time Lur'e systems with sector and slope bounded nonlinearities. By manipulating stability analysis conditions from the literature based on integralquadratic-constraint theory and multipliers, and applying Finsler's lemma, new synthesis conditions are provided in terms of sufficient linear matrix inequalities. After applying a relaxation in the stability conditions, an iterative algorithm is proposed to search for the two stabilizing gains of the control law, one for the output of the plant and one for the output of the nonlinear branch. The gains, that appear affinely in the inequalities, are treated as variables of the optimization problem. Therefore, the approach can handle state or output-feedback indistinctly and cope with magnitude or structural constraints (such as decentralization) in the gains without introducing additional conservatism. Numerical examples illustrate the results.

Modern network and communication technologies are essential for the implementation and operation of load frequency control (LFC) systems. The measurements of crucial LFC system parameters will be compromised by attackers, rendering data received by the defence inaccurate and causing frequency fluctuations or even system collapse. To detect the potential attack on measured data and keep the LFC performance, an adaptive event-triggered scheme with fractional order global sliding mode control scheme is proposed in this paper. Furthermore, Markov theory is employed for the modelling process with energy storage to present a multi‐area LFC power system considering renewable energy and hybrid cyber attacks. Stability and stabilisation criteria are built by employing improved Lyapunov stability theory and second‐order Bessel‐Legendre inequality. Finally, a two‐area LFC system under hybrid cyber attacks and a modified IEEE 39‐bus New England test power system with 3 wind farms are simulated to explore the efficacy of the proposed method.

This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system.

International audience; This paper addresses the problem of eventtriggered control (ETC) of discrete-time linear time-invariant (LTI) systems stabilized by neural network controllers. The event-triggering mechanisms (ETMs) is proposed to update only a portion of the layers required to maintain stability and satisfactory performance of the feedback system, thus reducing the computational cost associated with the evaluation of the neural network. Sufficient convex conditions in the form of linear matrix inequalities (LMIs) are provided to compute the triggering parameters and characterize an estimate of the domain of attraction for the feedback system. The formulation is based on the use of Lyapunov theory and a set of generalized sector constraints that deal with the nonlinear activation functions, represented in this case by the saturation function. Optimization procedures are also formulated to effectively reduce the amount of computation in the neural network. An example borrowed from the literature is used to illustrate the effectiveness of the proposal.

Publisher Copyright: Author This paper considers a formulation of the robust adaptive beamforming (RAB) problem based on worst-case signal-to-interference-plus-noise ratio (SINR) maximization with a nonconvex uncertainty set for the steering vectors. The uncertainty set consists of a similarity constraint and a (nonconvex) double-sided ball constraint. The worst-case SINR maximization problem is turned into a quadratic matrix inequality (QMI) problem using the strong duality of semidefinite programming. Then a linear matrix inequality (LMI) relaxation for the QMI problem is proposed, with an additional valid linear constraint. Necessary and sufficient conditions for the tightened LMI relaxation problem to have a rank-one solution are established. When the tightened LMI relaxation problem still has a high-rank solution, the LMI relaxation problem is further restricted to become a bilinear matrix inequality (BLMI) problem. We then propose an iterative algorithm to solve the BLMI problem that finds an optimal/suboptimal solution for the original RAB problem by solving the BLMI formulations. To validate our results, simulation examples are presented to demonstrate the improved array output SINR of the proposed robust beamformer.

Diese Dissertation präsentiert neue Ergebnisse zur kooperativen Regelung von Fahrzeugen. Modulare Architekturen werden untersucht, die aus Netzwerken vereinfachter Modelle und komplexer Fahrzeuge bestehen, die die von diesen vereinfachten Modellen erzeugten Trajektorien verfolgen. Dissipativitätstheorie und \textit{integral quadratic constraints} werden verwendet, um hinreichende Bedingungen für Stabilität und Regelgüte zu finden, die höchstens linear mit der Netzwerkgröße skalieren. Konvexe und nicht-konvexe Interaktionen zwischen Fahrzeugen werden im Zusammenhang mit einem \textit{source-seeking} Problem betrachtet, bei dem Fahrzeuge das Minimum eines externen Skalarfelds lokalisieren müssen. Experimente mit Quadrotoren und Simulationsstudien veranschaulichen die Ergebnisse., This thesis presents results on cooperative control of vehicles by studying modular architectures consisting of networks of simplified models and complex vehicles tracking the trajectories generated by these simplified models. Convex intervehicle interactions from formation control and non-convex inter-vehicle interactions emerging from flocking dynamics are studied within the context of a source-seeking problem, where vehicles are required to locate the minimum of an external scalar field. The main analysis tools are dissipativity theory and integral quadratic constraints while the experimental results are with quadrotors.

In modern smart manufacturing, robots are often connected via a network, and their task can change according to a predetermined program. Iterative learning control (ILC) is widely used for robots executing high-precision operations. Under network conditions, the efficiency of ILC algorithms may decrease if the program is restructured. In particular, the learning error may temporarily increase to an unacceptable value when changing the reference trajectory. This paper considers a networked system with the following features: the reference trajectory and parameters change between passes according to a known program, agents are subjected to random disturbances, and measurements are carried out with noise. In addition, the network topology changes due to the disconnection of some agents from the network and the connection of new agents to the network according to a given program. A distributed ILC design method is proposed based on vector Lyapunov functions for repetitive processes in combination with Kalman filtering. This method ensures the convergence of the learning error and reduces its increase caused by changes in the reference trajectory and network topology. The effectiveness of the proposed method is confirmed by an example., Automation and Remote Control, Выпуск 6 2023

In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model., Comment: 32 pages, 13 figures. Submitted to IEEE Transactions on Automatic Control

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. Part II of this paper explores further implications of the results in Part I. We present a necessary and sufficient LMI condition for the feasibility of a vector of power demands (under small perturbation), which extends a necessary condition in the literature. The alternatives of these LMI conditions are also included. In addition we refine these LMI conditions to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which allows for an alternative approach to determine power flow feasibility. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. Finally, we prove that the unique long-term voltage semi-stable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is obtained, as well as a parametrization of the boundary of the set of feasible power demands.

This paper considers a linear discrete-time system operating in a repetitive mode to track a reference trajectory with a required accuracy. The control variable has a delay along the sample trajectory, and saturation-type constraints are imposed. We introduce a new method for designing an iterative learning control law that depends on the delay and ensures the required accuracy of tracking. A numerical example demonstrates the effectiveness of this method., Automation and Remote Control, Выпуск 1 2023, Pages 82-95

Одной из важнейших характеристик переходного процесса в линейных динамических системах при ненулевых начальных условиях является величина максимального отклонения траектории от нуля, имеющая непосредственный инженерный смысл. Если ее значение велико, говорят о наличии эффекта всплеска. Статья завершает серию работ, посвященных исследованию эффекта всплеска в линейных системах управления. Рассматривается линейная система управления, подверженная воздействию неслучайных ограниченных внешних возмущений и системных неопределенностей. Предложен регулярный подход к синтезу стабилизирующей статической обратной связи, минимизирующей величину отклонения. Подход основан на технике линейных матричных неравенств и предполагает сведение исходной задачи к параметрической задаче полуопределенного программирования, легко решающейся численно. Предложенный подход может быть распространен на новые классы задач, в частности – на случай обратной связи по выходу системы с использованием наблюдателя или динамического регулятора., A major characteristic of transients in linear dynamic systems with non-zero initial conditions is the maximum deviation of the trajectory from zero, which has a direct engineering meaning. If the maximum deviation is large, the so-called peak effect occurs. This paper completes a series of research works devoted to the peak effect in linear control systems. We consider a linear control system with non-random bounded exogenous disturbances and system uncertainties. A regular approach is proposed to design a stabilizing static state-feedback control law that minimizes the peak effect. The approach is based on the technique of linear matrix inequalities and reduces the original problem to a parameterized semidefinite programming one, which can be easily solved numerically. The proposed approach can be extended to new classes of problems, in particular, to the case of output feedback using an observer or a dynamic controller., Проблемы управления, Выпуск 3 2023, Pages 2-19

As shown below, the linear operator norms in the deterministic and stochastic cases are optimal values of the Lagrange-dual problems. For linear time-varying systems on a finite horizon, the duality principle leads to stochastic interpretations of the generalized H2 and H1 norms of the system. Stochastic minimax filtering and control problems with unknown covariance matrices of random factors are considered. Equations of generalized H1-suboptimal controllers, filters, and identifiers are derived to achieve a trade-off between the error variance at the end of the observation interval and the sum of the error variances on the entire interval., Automation and Remote Control, Выпуск 2 2023

Исследуются нелинейные законы управления, полученные из линейного путем двух типов замен с использованием нечетных функций. Первая замена состоит в пропускании каждой компоненты вектора состояния через нелинейную функцию, вторая замена -- в пропускании всего линейного закона управления через нелинейную функцию. Для исследования таких систем предлагается представить нелинейные функции в виде линейных с нелинейным угловым коэффициентом. Такое представление позволит использовать аппарат линейных матричных неравенств (ЛМН) для исследования устойчивости замкнутых систем. Найдены области устойчивости и области для начальных условий, полученные в результате многошаговой процедуры поиска решений с использованием ЛМН. Показано, что использование предложенных нелинейных законов управления позволяет уменьшить установившуюся ошибку по сравнению с линейным. Приведены многочисленные моделирования, иллюстрирующие теоретические выводы., The paper investigates nonlinear control laws obtained from linear one by two types of coordinate change by using odd functions. The first coordinate change consists in passing each component of the state vector through a nonlinear function, the second coordinate change is in passing the entire linear control law through a nonlinear function. To study such systems, it is proposed to represent nonlinear functions as linear ones with a nonlinear slope. Such a representation will allow using the methods of linear matrix inequalities (LMI) to study the stability of the closed-loop systems. The stability domains and the domains for the initial conditions are found, obtained as a result of a multi-step solution search procedure using LMI. It is shown that the use of the proposed nonlinear control laws makes it possible to reduce the steady-state error compared to the linear one. The simulations illustrate the theoretical conclusions., Управление большими системами: сборник трудов, Выпуск 102 2023, Pages 58-75

International audience; This paper focuses on the anti-windup design for saturated one-dimensional linear reaction-diffusion equation. The considered open-loop system admits a finite number of unstable poles. We consider a scenario in which the system is controlled via a dynamic, finite-dimensional output feedback controller ensuring closed-loop exponential stability. Within this setting, a method is proposed to design a dynamic, finitedimensional anti-windup compensator to maximize the region of attraction and minimize the effect of external perturbations. More precisely, the sufficient conditions for the local exponential stability of the closed-loop system are derived and expressed in terms of a set of matrix inequalities. Using generalized sector conditions and proper change of variables, the conditions are then recast as an optimization problem solving linear matrix inequalities. A numerical example is provided to showcase the proposed method and highlight its effectiveness on the system performance.

This paper presents a novel approach for designing reconfiguration blocks for fault hiding of linear systems subject to actuator faults based on the passivity/dissipativity theory. For this purpose, the concept of passivation block is used to design virtual actuators (VAs) which guarantee that the faulty plant achieves the desired passivity indices and consequently the stability. Linear matrix inequalities (LMI)-based conditions are provided for designing the proposed VAs for ensuring the stability recovery for linear systems. Finally, a numerical example is used for assessing the proposed approach., This work was supported by the Brazilian agencies CNPq, FAPEMIG, FAPEAM, and the PROPG-CAPES/FAPEAM Scholarship Program. This work has also been partially co-financed by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. MINECO PID2020-114244RB-I00) and the ERDF Operational Program of Catalonia 2014-2020 (ref. 001-P-001643 Looming Factory).

International audience; The basal metabolic rate characterizes the energy consumption of the human body at rest. It can be estimated by using respiratory gas exchange analyzers and indirect calorimetry. During cycling this value could vary due to several adaptation processes such as an increase in breathing and blood circulation, controlling body temperature, among others. In this paper we propose to reconstruct the instantaneous value of this basal metabolic rate, referred here as basal power (measured in Watts), by using a robust discrete-time proportional integral (PI) observer. The observer design is based on a solution of linear matrix inequalities and uses an uncertain linear parameter varying model of the gas exchange dynamics. The proposed methodology allows the reconstruction of the basal power while making the respiratory gas exchange estimation robust to bounded uncertainties and disturbances. The PI observer has been validated in simulation.

Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases. Funding Agencies|Center for Industrial Information Technology at Linkoping University [17.12]; Industry Excellence Center LINK-SIC - Swedish Governmental Agency for Innovation Systems; Saab AB; Project Scalable Kalman filters - Swedish Research Council

This paper proposes a new filtering scheme applied to a linearized model of a nonlinear representation for combustion systems, whose parameters are obtained by means of optical sensors. To ensure a robust representation regarding the chosen operation point and external disturbances variations, a linear parameter-varying (LPV) state-space representation is proposed in terms of noise disturbances and time-varying parameters affecting the plant (like the instrumentation noise and non-laminar air flow). Concerning the proposed filtering scheme, a new observer structure, which includes the incorporation of the control signal as an additional input of the filter, is proposed to assure improved stability margins and performance given in terms of the H∞ norm. The filter design method is based on a convex optimization technique and is capable to deal with unstable dynamics. A numerical experiment, whose data were obtained from an actual combustion plant, illustrates the flexibility and advantages of the method when compared with the maximum correntropy criterion based Kalman filter, the full-order filter and the standard Luenberger observer.

In this letter, a robust quantized sampled–data controller is provided for a class of nonlinear systems affected by time–varying uncertainties, actuation disturbances and measurement noises. Sufficient conditions based on linear matrix inequalities and ensuring the existence of the proposed robust quantized sampled–data controller are given. Quantization of both state measurements and input signals is simultaneously considered. Input–to–state stability redesign technique is used in order to attenuate the effects of bounded actuation disturbances and of bounded observation errors. It is proved that, under suitably fast sampling and accurate quantization of the input/output channels, the proposed controller achieves the semi–global practical stability, with arbitrarily small final target ball, of the related quantized sampled–data closed–loop system provided that the observation errors do not affect (or affect marginally) the robustification term added in the controller and, that the bounds of the actuation disturbances as well as of the observation errors are a priori known. The theory here developed includes also the cases of time–varying sampling intervals and of non–uniform quantization of the input/output channels as well as the stability analysis of the inter–sampling system behavior. The provided results are validated through an example of one–link manipulator.

International audience; This letter addresses an unknown input observer design to estimate simultaneously the 3D depth of a tracked image feature and the camera linear velocity using a low cost monocular camera and inertial sensor. The camera kinematic model is at first, augmented via the dynamic extension approach then described as a quasi-Linear Parameter Varying (qLPV) model. Further, the qLPV system is transformed into Takagi-Sugeno (T-S) form with unmeasured premise variables. The error convergence analysis is performed based on Lyapunov theory and Input to State Stability (ISS) property to ensure the boundedness of the state estimation error. Gains that guarantee the asymptotic stability of the estimation error can be properly computed by means of Linear Matrix Inequalities (LMIs). Finally the proposed approach is validated using synthetic data.

In this paper, we investigate the interval observer problem for a class of discrete-time nonlinear systems, in absence or presence of external disturbances and parametric uncertainties. The interval observers depend on the design of two preserving order observers, providing lower and upper estimations of the state. The main objective is to apply the stability radii notions and cooperativity property in the estimation error systems in order to guarantee that the lower/upper estimation is always below/above the real state trajectory at each time instant from an appropriate initialization, and the estimation errors converge asymptotically towards zero when the disturbances and/or uncertainties are vanishing. For the disturbed case, the estimation errors practically converge to a vicinity of zero, while the lower/upper estimations preserve the partial ordering with respect to the state trajectory. The design conditions, that are valid for Lipschitz nonlinearities, can be expressed as Linear Matrix Inequalities (LMIs). A numerical simulation example is provided to verify the effectiveness of the proposed method.

Made available in DSpace on 2022-05-01T09:31:06Z (GMT). No. of bitstreams: 0 Previous issue date: 2022-02-01 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) In this work, a robust switched controller design using output feedback is proposed. The minimization of the output energy is taken into account as a design strategy to reduce the settling time and oscillations of the closed-loop system output. In the design of the controllers, physical limits of the system outputs are also covered, which is done by considering a convex set of initial conditions. Sufficient LMI conditions to solve the control design are presented in the form of theorems that require the choice of constant parameters. The search for the most adequate parameters was accomplished via the differential evolution algorithm. Moreover, the proposed switched controller design is compared with a constant output feedback gain controller and other methodologies proposed in the literature. Theoretical analyses, two numerical examples and a practical implementation in an active suspension system were carried out to show the advantages of the proposed methodology. São Paulo State University (UNESP) School of Engineering, Ilha Solteira, José Carlos Rossi Avenue, 1370 IFPR – Federal Institute of Education Science and Technology of Paraná Campus of Jacarezinho Jacarezinho IFMS – Federal Institute of Education Science and Technology of Mato Grosso do Sul Campus of Campo Grande São Paulo State University (UNESP) School of Engineering, Ilha Solteira, José Carlos Rossi Avenue, 1370 CAPES: 001 CNPq: 120545/2020-9 FAPESP: 2011/17610-0 CNPq: 301227/2017-9 CNPq: 309872/2018-9

Power system stability is greatly affected by two types of stochastic or random disturbances: (1) topological and (2) parametric. The topological stochastic disturbances due to line faults caused by a series of lightning strikes (associated with circuit breaker, C.B., opening, and auto-reclosing) are modeled in this paper as continuous-time Markov jumps. Additionally, the stochastic parameter changes e.g., the line reactance, are influenced by the phase separation, which in turn depends on the stochastic wind speed. This is modeled as a stochastic disturbance. In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. The invariant ellipsoid and linear matrix inequality (LMI) optimization are used to construct the control system. The numerical simulations are presented on a multi-machine test system.

In this study, an unknown input observer (UIO) is developed in explicit form to estimate unmeasurable states and unknown inputs (UIs) for nonlinear implicit systems represented by the discrete-time Takagi-Sugeno implicit systems (DTSIS) in the case of unmeasurable premise variables. The method employed is based on singular value decomposition (SVD) and augmenting the state vector, which is formed partly by the system state and partly by the UIs. The convergence of the augmented state estimation error is provided by a Lyapunov function ending with solving the linear matrix inequalities (LMI). An application to a model of the rolling disc is considered to evaluate the effectiveness of the developed approach. It appears that estimated variables converge to the true variables quickly and accurately.

The problem of unknown input observer design is considered for coupled PDE/ODE systems subject to incremental sector bounded nonlinearities and unknown boundary inputs. Assuming available measurements at the boundary of the distributed domain, the synthesis of the unknown input observer is based on Lyapunov methods and convex optimization. Numerical simulations support and confirm the theoretical findings, illustrating the robust estimation performances of the proposed nonlinear unknown input observer., Extended version of the paper to appear in the IEEE Transactions on Automatic Control

Introduction. Fault diagnosis, and fault tolerant control issues are becoming very important to ensure a good supervision of systems and guarantee the safety of human operators and equipments even if system complexity increases. Problem. In fact, the presence of faults in actuators, sensors and processes can lead to system performance degradation, system breakdown, economic loss, and even disastrous situations. Furthermore, Actuator saturation or control input saturation is probably the most usual nonlinearity encountered in control engineering because of the physical impossibility of applying unlimited control signals and/or safety constraints. Purpose. This article is dedicated to the problem of fault tolerant control for constrained nonlinear systems described by a Takagi-Sugeno model. One of the interests of this type of models is the possibility of extend some tools and methods from linear system case to the nonlinear one. The novelty of the work consists in developing a fault tolerant control algorithm for a nonlinear Permanent Magnet Synchronous Machine model using an observer based state-feedback control technique in order to enhance fault and state estimation despite actuator saturation and system disturbances. Methods. Indeed a sensor fault detection observer based residual generator is synthesized with a guaranteed L2 performance to attenuate the external disturbances effect from one side and to maximize the residual sensitivity to faults from the other side. Based on Lyapunov function, design conditions are formulated in terms of Linear Matrix Inequalities to ensure stability of the global system. Practical value. A detailed study concerning nonlinear permanent magnet synchronous machine model, which is consolidated by simulation results, is conducted to show the used algorithm’s effectiveness guarantying fault estimation and reconfiguration of the control law to maintain stable performance even in the presence of actuator faults, external perturbation and the phenomenon of actuator saturation., Вступ. Діагностика несправностей і питання стійкості до відмови стають дуже важливими для забезпечення хорошого контролю систем і гарантії безпеки людей-операторів і обладнання, навіть якщо складність системи зростає. Проблема. Насправді наявність несправностей у виконавчих механізмах, датчиках і процесах може призвести до зниження продуктивності системи, поломки системи, економічних втрат і навіть катастрофічних ситуацій. Крім того, насичення виконавчого механізму або насичення керуючого входу, ймовірно, є найбільш поширеною нелінійністю, що зустрічається в техніці керування через фізичну неможливість застосування необмежених керуючих сигналів та обмежень безпеки. Мета. Ця стаття присвячена проблемі стійкості до відмови нелінійних систем з обмеженнями, що описуються моделлю Такагі-Сугено. Однією з переваг цього типу моделей є можливість поширення деяких інструментів та методів з випадку лінійної системи на нелінійну. Новизна роботи полягає у розробці алгоритму управління стійкості до відмови для моделі нелінійної синхронної машини з постійними магнітами з використанням методу управління зі зворотним зв'язком станом на основі спостерігача, щоб поліпшити оцінку помилок і станів, незважаючи на насичення приводу і збурення системи. Методи. Дійсно, генератор нев'язки на основі спостерігача виявлення несправності датчика синтезується з гарантованою продуктивністю L2, щоб послабити вплив зовнішніх перешкод з одного боку та максимізувати залишкову чутливість до несправностей з іншого боку. На основі функції Ляпунова умови проєктування формулюються в термінах лінійних матричних нерівностей для забезпечення стійкості глобальної системи. Практична цінність. Детальне дослідження нелінійної моделі синхронної машини з постійними магнітами, об'єднане результатами моделювання, проводиться для демонстрації ефективності використовуваного алгоритму, що гарантує оцінку відмов та реконфігурацію закону управління для підтримки стабільної роботи навіть за наявності відмов приводу, зовнішніх збурень та явища насичення приводу.

The objective of this work is to design a Nonlinear Observer used in a Cascade Control scheme for Maximum Power Point Tracking goals of a grid-tied single-phase photovoltaic inverter. The main contribution of this work is to employ a nonlinear observer to reduce the number of sensors of an AC-grid-tied single-stage PV system. The nonlinear observer design was developed using the Takagi-Sugeno PV system model and Linear Matrix Inequalities based on Lyapunov stability criteria. To validate the performance of the nonlinear observer-based cascade control, the results of a comparison between the PV system with observer (without DC voltage sensor) and a PV system with DC voltage sensor (without observer) are presented. A suitable PV power estimation with the nonlinear observer-based cascade control is achieved, which allowing a good performance of the MPPT algorithms. Perturb & Observe and Incremental Conductance MPPT algorithms were used.

The linear parameter-varying (LPV) models have broad applications in advanced mathematics and modern control systems. This paper introduces a new method for controlling the LPV systems. This method includes the gain-scheduled state-feedback technique and a fuzzy system to calculate the state-feedback gain. The main goal of the control system is to stabilize the system and bring its states to equilibrium points. Linear matrix inequalities calculate feedback gains to stabilize the system. On the other hand, a fuzzy control system also produces a combined signal with the primary controller signal to speed up this operation. Lyapunov’s theory is used to guarantee the control system’s stability. Finally, to evaluate the performance of the proposed control system, the inverted pendulum has been investigated as a case study. The results show that the proposed method has good efficiency and performance.

This paper studies the consensus control problem of multiple high-speed trains with nonlinear running resistance based on a distributed event-triggered control protocol. Firstly, the multiple high-speed trains are established as a multi-agent model with a leader–follower. For the system whose leader has an unknown input, the effective state observers are introduced to observe the state of the train. Then, an observer-based event-triggered strategy is designed to determine the time when the train state is transmitted to the local controller and adjacent trains. The proposed control scheme is based on local information, and the solutions of the state observer and the gain symmetric matrices parameters of the distributed event-triggered control strategy are constructed in the form of linear matrix inequalities (LMI). Through the Lyapunov stability theory, sufficient conditions for the stable and safe operation of multiple high-speed trains systems are obtained. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

The main topic of this work is to investigate the delayed nonquadratic zonotopic interval estimation for discrete-time nonlinear systems in the Takagi-Sugeno’s (T-S) form. Due to the improvements made to traditional quadratic methods, the estimation accuracy is enhanced and the conservatism is efficiently reduced. Firstly, based on multiple sums and multisets of delays, an overall nonquadratic zonotopic estimation framework with tuneable delayed terms is proposed for T-S fuzzy systems. A general observer gain computation method with L∞ performance is derived in terms of matrix inequalities shortly afterward. The design conditions are relaxed by selecting a group of specific multisets of delays that the observer gain acquisition problem is transformed into solving a set of linear matrix inequalities (LMIs). Furthermore, the rules for selecting appropriate multisets of delays, which limit the computational complexity and improve the design freedom, are analyzed. Finally, two examples illustrate the feasibility, effectiveness, and practicability of the proposed method., Graduate School of Mie University, 52p

International audience; This paper investigates the problems of stability analysis and control design for continuoustime Lur'e systems with slope bounded nonlinearities. Starting from a stability analysis condition from the literature, based on the real positivity and a bound to the L 1 norm of a certain transfer function, new sufficient conditions are proposed in an augmented parameter space for the simultaneous existence of a stabilizing dynamic output-feedback controller and a Zames-Falb multiplier certifying the closed-loop stability. The matrices of the controller realization as well as of the Zames-Falb multiplier appear affinely in the conditions, being dealt with as optimization variables. Furthermore, no line search is required to enforce the L 1 norm constraint. An iterative algorithm is constructed to solve the problem through semidefinite programming, providing dynamic controllers of any given order. The controller can take into account both the output of the linear part of the system and of the nonlinearity. Numerical examples illustrate the results.

Infinite dimensional systems allow to model a large panel of physical phenomena for which the state variables evolve both temporally and spatially. This manuscript deals with the evaluation of the stability of their equilibrium point. Two case studies are treated in particular: the stability analysis of ODE-transport, and ODE-reaction-diffusion interconnected systems. Theoretical tools exist for the stability analysis of these infinite-dimensional linear systems and are based on an operator algebra rather than a matrix algebra. However, these existence results raise a problem of numerical constructibility. During implementation, an approximation is performed and the results are conservative. The design of numerical tools leading to stability guarantees for which the degree of conservatism is evaluated and controlled is then a major issue. How can we develop reliable numerical criteria to rule on the stability or instability of infinite-dimensional linear systems? In order to answer this question, one proposes here a new generic method, which is decomposed in two steps. First, from the perspective of Legendre polynomials approximation, augmented models are built and split the original system into two blocks: on the one hand, a finite-dimensional approximated system is isolated, on the other hand, the infinite-dimensional truncation error is preserved and modeled. Then, frequency and time tools of finite dimension are deployed in order to propose stability criteria that have high or low numerical load depending on the approximated order. In frequencies, with the aid of the small gain theorem, sufficient stability conditions are obtained. In temporal, with the aid of the Lyapunov theorem, an under estimate of the stability regions is proposed as a linear matrix inequality and an over estimate as a positivity test. Our two case studies have been treated with this general methodology. The main result concerns the case of ODE-transport interconnected systems, for which the approximation and stability analysis using Legendre polynomials leads to exponentially fast converging estimates of stability regions. The method developed in this manuscript can be adapted to other types of approximations and exported to other infinite-dimensional linear systems. Thus, this work opens the way to obtain necessary and sufficient finite-dimensional conditions of stability for infinite-dimensional systems., Les systèmes de dimension infinie permettent de modéliser un large spectre de phénomènes physiques pour lesquels les variables d'états évoluent temporellement et spatialement. Ce manuscrit s'intéresse à l'évaluation de la stabilité de leur point d'équilibre. Deux études de cas seront en particulier traitées : l'analyse de stabilité des systèmes interconnectés à une équation de transport, et à une équation de réaction-diffusion. Des outils théoriques existent pour l'analyse de stabilité de ces systèmes linéaires de dimension infinie et s'appuient sur une algèbre d'opérateurs plutôt que matricielle. Cependant, ces résultats d'existence soulèvent un problème de constructibilité numérique. Lors de l'implémentation, une approximation est réalisée et les résultats sont conservatifs. La conception d'outils numériques menant à des garanties de stabilité pour lesquelles le degré de conservatisme est évalué et maîtrisé est alors un enjeu majeur. Comment développer des critères numériques fiables permettant de statuer sur la stabilité ou l'instabilité des systèmes linéaires de dimension infinie ? Afin de répondre à cette question, nous proposons ici une nouvelle méthode générique qui se décompose en deux temps. D'abord, sous l'angle de l'approximation sur les polynômes de Legendre, des modèles augmentés sont construits et découpent le système original en deux blocs : d'une part, un système de dimension finie approximant est isolé, d'autre part, l'erreur de troncature de dimension infinie est conservée et modélisée. Ensuite, des outils fréquentiels et temporels de dimension finie sont déployés afin de proposer des critères de stabilité plus ou moins coûteux numériquement en fonction de l'ordre d'approximation choisi. En fréquentiel, à l'aide du théorème du petit gain, des conditions suffisantes de stabilité sont obtenues. En temporel, à l'aide du théorème de Lyapunov, une sous-estimation des régions de stabilité est proposée sous forme d'inégalité matricielle linéaire et une sur-estimation sous forme de test de positivité. Nos deux études de cas ont ainsi été traitées à l'aide de cette méthodologie générale. Le principal résultat obtenu concerne le cas des systèmes EDO-transport interconnectés, pour lequel l'approximation et l'analyse de stabilité à l'aide des polynômes de Legendre mène à des estimations des régions de stabilité qui convergent exponentiellement vite. La méthode développée dans ce manuscrit peut être adaptée à d'autres types d'approximations et exportée à d'autres systèmes linéaires de dimension infinie. Ce travail ouvre ainsi la voie à l'obtention de conditions nécessaires et suffisantes de stabilité de dimension finie pour les systèmes de dimension infinie.

This paper presents a new approach to integral sliding mode control for discrete nonlinear systems with time delay. The approach is based on an event-triggered scheme and is applied to Takagi–Sugeno fuzzy models. In the first step, a new integral sliding function is constructed, which avoids the limited assumptions of most existing fuzzy sliding mode control schemes. The design parameter matrices defining the sliding surface are obtained by solving linear matrix inequalities. In the second step, an event trigger-based integral sliding mode control protocol is developed to ensure the state trajectories of the Takagi–Sugeno fuzzy systems with time delays. Finally, the proposed strategies are evaluated through a simulation example to demonstrate their effectiveness.

The objective of this paper focuses on the stability analysis of the input-output finite-time for a class of fractional-order switched singular systems (FOSSS) with D-perturbation. By using the Φ-dependent average dwell time (ΦDADT) approach together with the multiple Lyapunov functions method, some sufficient conditions are derived for the considered system to ensure its input-output finite-time stability in terms of linear matrix inequalities. Then, the output feedback controller is designed to ensure the closed-loop system is input-output finite-time stable. Finally, a numerical example illustrates the superiority of the proposed method.

Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. In the first part of the paper the feasible Filippov solution concept is introduced by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. Several examples illustrate the theoretical arguments and the effectiveness of the stability result.

CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Outra Agência Os processos industriais estão se tornando cada vez mais autônomos e complexos. Consequentemente, a demanda por segurança e confiabilidade desses processos é crescente. Nesse contexto, técnicas de controle tolerante a falhas (FTC, do inglês Fault-Tolerant Control) têm recebido bastante atenção ao longo das últimas décadas buscando fornecer redundância analítica e aumentar a confiabilidade desses sistemas. Esta tese aborda o problema de FTC para sistemas não-lineares baseado na abordagem de ocultação de falhas. A ocultação de falhas consiste na inserção de um bloco de reconfiguração (RB, do inglês Reconfiguration Block) entre a planta com falhas e o controlador. O RB mitiga os efeitos das falhas sem exigir reprojeto do controlador, do qual as falhas são ocultadas. Embora eficazes, a maioria das abordagens de ocultação de falhas na literatura não cobrem todas as classes de sistemas não-lineares, além de serem sensíveis a imprecisões na estimativa das falhas devido à dependência das estruturas canônicas de RB, conhecidas como sensores e atuadores virtuais, em relação ao princípio do modelo interno. Nesse sentido, esta tese aborda a ocultação de falhas para sistemas não-lineares baseada em novos RBs cujos parâmetros não dependem explicitamente do modelo de falhas. Para tal, condições suficientes baseadas em desigualdades matriciais lineares (LMIs, do inglês Linear Matrix Inequalities) são apresentadas para o projeto de RBs que garantam a recuperação da estabilidade. Para obter essas condições, três novas classes de abordagens são propostas, a saber: uma abordagem baseada em Lyapunov em que uma função de Lyapunov é obtida em uma etapa de análise do sistema nominal e, em seguida, é usada para projetar os RBs para recuperação de estabilidade do sistema reconfigurado em uma etapa de síntese; uma abordagem baseada em dissipatividade na qual as desigualdades de dissipação são obtidas em uma etapa de análise para o sistema nominal e, em seguida, são usadas para projetar os RBs para recuperação de dissipatividade do sistema reconfigurado em uma etapa de síntese; finalmente, uma abordagem baseada em passivação é proposta para obter RBs cuja dissipatividade compensem a falta de passividade devido à ocorrência de falhas. Industrial processes and technological systems are becoming more and more autonomous and complex. Consequently, the demand for the safety and reliability of these systems is increasing. In this context, process monitoring and fault-tolerant control (FTC) have received a lot of attention during the last decades to provide analytical redundancy to these processes and improve their reliability. This thesis addresses the problem of FTC for nonlinear systems based on the fault hiding approach. Fault hiding consists in inserting a reconfiguration block (RB) between the faulty plant and the controller. The RB mitigates the fault effects by dispensing with the controller redesign, through recovering sensor measurements and reallocation of the control effort required by a controller that does not receive the information about the fault occurrence. Although effective, most of the fault hiding approaches available in the literature do not cover all classes of nonlinear systems, and they are sensitive to fault estimation inaccuracy because the canonical RB structures, known as virtual sensors and actuators, rely on the internal model principle. In this sense, this thesis addresses the problem of fault hiding for nonlinear systems based on novel RB structures whose parameters do not exhibit explicit dependence on the fault model. This thesis presents a novel constructive design with sufficient conditions based on linear matrix inequalities (LMIs) for guaranteeing stability recovery by fault hiding. For obtaining those conditions, three novel classes of approaches are proposed, namely: a Lyapunov-based approach wherein a Lyapunov function is obtained in a stability analysis step for the nominal system, then it is used to design the RBs for stability recovery of the reconfigured system in a synthesis step; a dissipativity based approach wherein dissipation inequalities are obtained in an analysis step for the nominal system, then they are used to design the RBs for dissipativity recovery of the reconfigured system in a synthesis step; finally, a passivation-based fault hiding approach is proposed to compute RBs with dissipativity properties which compensate for the lack of passivity of the closed-loop system due to the fault occurrence.

This paper presents a new control technique based on uncertain fuzzy models for handling uncertainties in nonlinear dynamic systems. This approach is applied for the stabilization of a multimachine power system subject to disturbances. In this case, a state-feedback controller based on parallel distributed compensation (PDC) is applied for the stabilization of the fuzzy system, where the design of control laws is based on the Lyapunov function method and the stability conditions are solved using a linear matrix inequalities (LMI)-based framework. Due to the high number of system nonlinearities, two steps are followed to reduce the number of fuzzy rules. Firstly, the power network is subdivided into sub-systems using Thevenin’s theorem. Actually, each sub-system corresponds to a generator which is in series with the Thevenin equivalent as seen from this generator. This means that the number of sub-systems is equal to the number of system generators. Secondly, the significances of the nonlinearities of the sub-systems are ranked based on their limits and range of variation. Then, nonlinearities with non-significant variations are assumed to be uncertainties. The proposed strategy is tested on the Western systems coordinating council (WSCC) integrated with a wind turbine. The disturbances are assumed to be sudden variations in wind power output. The effectiveness of the suggested fuzzy controller is compared with conventional regulators, such as an automatic voltage regulator (AVR) and power system stabilizers (PSS).

[EN] This paper investigates the exponential stability of uncertain time delay systems using a novel descriptor redundancy approach based on delay partitioning. First, the original system is casted into an equivalent descriptor singular state¿space representation by introducing redundant state variables so that the resulting delay is progressively reduced. From the equivalent model and applying Lyapunov Functional method, a sufficient condition based on Linear Matrix Inequalities (LMIs) for exponential stability with guaranteed decay rate performance is obtained. As a result, the inherent conservatism of Lyapunov¿Krasovskii functional techniques can arbitrarily be reduced by increasing the number of delay partition intervals including decay rate performance and model uncertainties in polytopic form. Various benchmark examples are provided to validate the effectiveness of the proposed method, showing better trade-off between conservatism and performance in comparison to previous approaches., This work was supported by project PGC2018-098719-B-I00 (MCIU/AEI/FEDER,UE).