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Recent developments in communication technologies, such as 5G, together with innovative computing paradigms, such as edge computing, provide further possibilities for the implementation of real-time networked control systems. However, privacy and cyber-security concerns arise when sharing private data between sensors, agents and a third-party computing facility. In this paper, a secure version of the distributed formation control is presented, analyzed and simulated, where gradient-based formation control law is implemented in the edge, with sensor and actuator information being secured by fully homomorphic encryption method based on learning with error (FHE-LWE) combined with a proposed mixed uniform-logarithmic quantizer (MULQ). The novel quantizer is shown to be suitable for realizing secure control systems with FHE-LWE where the critical real-time information can be quantized into a prescribed bounded space of plaintext while satisfying a sector bound condition whose lower and upper-bound can be made sufficiently close to an identity. An absolute stability analysis is presented, that shows the asymptotic stability of the closed-loop secure control system.

In this work we study and analyze a class of Duhem hysteresis operators that can exhibit butterfly loops. We study firstly the consistency property of such operator which corresponds to the existence of an attractive periodic solution when the operator is subject to a periodic input signal. Subsequently, we study the two defining functions of the Duhem operator such that the corresponding periodic solutions can admit a butterfly input-output phase plot. We present a number of examples where the Duhem butterfly hysteresis operators are constructed using two zero-level set curves that satisfy some mild conditions.

While it is widely used to represent hysteresis phenomena with unidirectional-oriented loops, we study in this article the use of Preisach operator for describing hysteresis behavior with multidirectional-oriented loops. This complex hysteresis behavior is commonly found in advanced materials, such as, shape-memory alloys or piezoelectric materials, that are used for high-precision sensor and actuator systems. We provide characterization of the Preisach operators exhibiting such input-output behaviors and we show the richness of the operators that are capable of producing intricate loops.

We present the design and experimental validation of source seeking control algorithms for a unicycle mobile robot that is equipped with novel 3D-printed flexible graphene-based piezoresistive airflow sensors. Based solely on a local gradient measurement from the airflow sensors, we propose and analyze a projected gradient ascent algorithm to solve the source seeking problem. In the case of partial sensor failure, we propose a combination of Extremum-Seeking Control with our projected gradient ascent algorithm. For both control laws, we prove the asymptotic convergence of the robot to the source. Numerical simulations were performed to validate the algorithms and experimental validations are presented to demonstrate the efficacy of the proposed methods., Published in IEEE Transactions on Robotics

We present three classes of distributed formation controllers for achieving and maintaining the 2D/3D formation shape of manipulator end-effectors to cope with different scenarios due to availability of modeling parameters. We firstly present a distributed formation controller for manipulators whose system parameters are perfectly known. The formation control objective is achieved by assigning virtual springs between end-effectors and by adding damping terms at joints, which provides a clear physical interpretation of the proposed solution. Subsequently, we extend it to the case where manipulator kinematic and system parameters are not exactly known. An extra integrator and an adaptive estimator are introduced for gravitational compensation and stabilization, respectively. Simulation results with planar manipulators and with seven degree-of-freedom humanoid manipulator arms are presented to illustrate the effectiveness of the proposed approach., Comment: arXiv admin note: text overlap with arXiv:2103.14595

This article focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses a heterogeneous sensing mechanism. For the setups consisting of three robots, we show that the use of heterogeneous gradient-based control laws can give rise to undesired invariant sets where a distorted formation shape is possibly moving at a constant velocity. We guarantee local asymptotic stability for the correct and desired formation shape. For the setup with one distance and two bearing robots, we identify the conditions such that an incorrect moving formation is locally attractive.

In this letter, we propose a contraction-based variable gain nonlinear control scheme for the laser-beam stabilizing (LBS) servo-system, which guarantees that the closed-loop system is convergent. With the variable gain acting on the velocity error, the well known waterbed effect of the low-frequency/bandwidth trade-off can be overcome. Moreover, the contraction-based framework allows us to extend the linear control performance metrics for analyzing the closed-loop nonlinear system behavior. The closed-loop system’s performance is evaluated in numerical simulations under input disturbances and/or white noise measurements and its efficacy is compared to that using PID and LQG controllers.

This paper deals with the synthesis and experimental performance evaluation of a contractivity-based nonlinear dynamic motion control scheme for a Laser-Beam Steering (LBS) system, which includes a saturated integral action and a variable gain. The variable gain, in the control law, is used to discriminate between “signal” and “noise” in the velocity measurements, allowing to do a trade-off between the low-frequency tracking and disturbance rejection properties and high-frequency measurement noise amplification, an effect known as waterbed effect. Then, the contractivity-based framework handles the stabilization problem together with the closed-loop performance, allowing one to generalize key properties of linear control systems to analyze transient and steady-state solutions performances in the nonlinear case. The proposed control scheme is evaluated on an experimental platform for the set-point regulation and trajectory tracking problems under different scenarios. Moreover, the effectiveness of the proposed control scheme is compared with linear controllers for the LBS system available in the literature.

We present a trajectory tracking control design method for a class of mechanical systems in the port-Hamiltonian framework. The proposed solution is based on the virtual contractivity-based control (v-CBC) method, which employs the notions of virtual systems and of contractivity. This approach leads to a family of asymptotic tracking controllers that are not limited to those that preserve the pH structure of the closed-loop system nor require an intermediate change of coordinates. Nevertheless, structure preservation and other properties (e.g., passivity) are possible under sufficient conditions. The performance of the proposed v-CBC scheme is experimentally evaluated on a planar robot of two degrees of freedom (DoF).

We present the design of H∞ and H2 gain-scheduled fault-accommodation controllers for discrete-time Linear Parameter Varying systems. We design our conditions as Bilinear Matrix Inequalities, assuming that the scheduled parameters are imprecise, which is a commonly found characteristic of practical applications that happens due to measurement noise and inaccuracy on its estimation/acquisition procedure. The proposed solution is based on the use of a multi-simplex approach for solving the main conditions, which guarantees the stability of the system under imprecise measurements on the scheduling parameters. The efficacy of the proposed approach is illustrated with a numerical example.

In this article, we study adaptation mechanisms in a class of phosphorylation cycles where allosteric binding and gene autoregulation mechanisms regulate the phosphorylation processes. We show that both mechanisms enable a robust setpoint regulation of the regulator metabolite in the presence of constant, as well as periodic, external stimuli. The allosteric binding mechanism without the presence of gene autoregulation can serve as an integral controller. Furthermore, we show that the incorporation of a gene autoregulation mechanism enables the gene expression system to act as a genetic oscillator, which allows for the adaptation mechanism to periodic external stimuli. These results provide a theoretical explanation to the cell homeostasis under quasi-constant environmental conditions, as well as periodic, biological rhythms.

In this work we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots (FJRs) in the port-Hamiltonian (pH) framework. The proposed design method, called virtual contraction based control (v-CBC), combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits properties such as structure preservation, differential passivity and the existence of (incrementally) passive maps., Comment: 10 pages, 4 figures, journal paper

This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with $m$-dimensional input space, it is sufficient to have $m+1$ discrete input points (other than zero for general passive systems or the target constant input for incrementally passive systems). Furthermore, we present a constructive algorithm to design such $m+1$ nonzero input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control., Comment: 13 pages, double-column, journal submission, revised version

In this paper, we tackle the fault-compensation controller in the context of Marko-vian Jump Linear Systems (MJLS). More specifically, we propose the design of H∞ Fault-Compensation Controllers under the MJLS formulation, which is provided in terms of linear matrices inequalities optimization problems. These particular controllers have as the main motivation the network communication loss which is inherent to any automation process. We present a numerical example of a coupled tank system, where a Monte Carlo simulation illustrates the feasibility of the proposed solution. The results show that the proposed approach is indeed a valuable alternative to compensate for the fault occurrence.

In this paper, we propose a new robustness notion that is applicable for certifying systems' safety with respect to external disturbance signals. The proposed input-to-state safety (ISSf) notion allows us to certify systems' safety in the presence of the disturbances which is analogous to the notion of input-to-state stability (ISS) for analyzing systems' stability., 9 pages, pre-print submitted to Automatica

Using recent results on the incremental stability analysis via contraction and on internal model principle, we revisit the pinning synchronization problem in nonlinear multi-agent systems (MAS). We provide sufficient and necessary conditions for both the pinned agents as well as the rest of the agents to guarantee the state synchronization. For the non-pinned agents, we present a distributed control framework based only on the relative local state measurement and we give sufficient conditions for the contractivity of the individual virtual systems in order to achieve pinning synchronization. Numerical simulation is given to illustrate the main results.

In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior angle measurements of the neighboring robots' disk, which can be obtained from low-cost vision sensors, we propose a gradient-based distributed control law and show the exponential convergence property of the associated error system. By construction, the proposed control law has the appealing property of ensuring collision avoidance between neighboring robots. We also present simulation results for {a team} of four circular mobile robots forming a rectangular shape., 6 pages, submitted to the 59th IEEE Conf. Dec. Control and IEEE Control Systems Letters

We tackle the fault accommodation control (FAC) in the Markovian jump linear system (MJLS) framework for the discrete-time domain, under the assumption that it is not possible to access the Markov chain mode. This premise brings some challenges since the controllers are no longer allowed to depend on the Markov chain, meaning that there is an asynchronism between the system and the controller modes. To tackle this issue, a hidden Markov chain ((Formula presented.), (Formula presented.)) is used where θ(k) denotes the Markov chain mode, and (Formula presented.) denotes the estimated mode. The main novelty of this work is the design of H∞ and H2 FAC under the MJLS framework considering partial observation of the Markov chain. Both designs are obtained via bilinear matrix inequalities optimization problems, which are solved using coordinate descent algorithm. As secondary results, we present simulations using a two-degree of freedom serial flexible joint robot to illustrate the viability of the proposed approach.

International audience; We study the relationship between the global exponential stability of an invariant manifold and the existence of a semi-definite positive Riemannian metric which is contracted by the flow. In particular, we investigate how the following properties are related to each other (in the global case): i). A manifold is globally ‘‘transversally’' exponentially stable; ii). The corresponding variational system (c.f. (8) in Section II) admits the same property; iii). There exists a degenerate Riemannian metric which is contracted by the flow and can be used to construct a Lyapunov function. We show that the transverse contraction rate being larger than the expansion of the shadow on the manifold is a sufficient condition for the existence of such a Lyapunov function. An illustration of these tools is given in the context of global full-order observer design.

Ultra-high vacuum chemical vapor deposition is a thin film deposition process that features excellent film purity, but is sensitive to the processing variations (such as, the precursors and their dispensers, the reactor’s initial condition, etc.). In this paper, we present the design of a ultra-high vacuum chemical vapor deposition reactor with in situ partial pressure atomic absorption spectroscopy measurement that improves reproducibility and observability of such a process. Our main contributions are: (i) a conceptual control systems design of ultra-high vacuum chemical vapor deposition; (ii) atomic absorption spectroscopy based sensor design for the real-time in situ partial pressure measurements; (iii) a flux dynamical model; (iv) experimental reactor design; and (v) experimental validation of model components and the atomic absorption spectroscopy measurement technique. Our results show that the proposed sensor systems are able to provide real-time measurements of the partial pressure inside the reactor and our proposed flux dynamical model agrees with the measured partial pressure. The latter allows us to use it in the design of model-based output feedback control of the partial pressure.

We present the conceptual design and initial development of the Hysteretic Deformable Mirror (HDM). The HDM is a completely new approach to the design and operation of deformable mirrors for wavefront correction in advanced imaging systems. The key technology breakthrough is the application of highly hysteretic piezoelectric material in combination with a simple electrode layout to efficiently define single actuator pixels. The set-and-forget nature of the HDM, which is based on the large remnant deformation of the newly developed piezo material, facilitates the use of time division multiplexing (TDM) to address the single pixels without the need for high update frequencies to avoid pixel drift. This, in combination with the simple electrode layout, paves the way for upscaling to extremely high pixel numbers ($\geq 128\times 128$) and pixel density ($100/mm^2$) deformable mirrors (DMs), which is of great importance for high spatial frequency wavefront correction in some of the most advanced imaging systems in the world.

In this paper, we analyze next generation sequencing (NGS) data of wastewater treatment plant (WWTP) in the North Water facility for revealing the role of 1236 different genera of microorganisms in the aeration basin to the measured process data. Both the time-series data of NGS and process parameters are pre-processed and analyzed using support vector regression technique and is compared with the deep neural network approach. Local sensitivity analysis is performed on the resulting models. Both machine learning analyses show the importance of a subset of genera to the WWTP process and can be used to enrich / to adapt the well-studied activated sludge model (ASM).

International audience; This article addresses output feedback stabilization of continuous-time nonlinear systems by choosing control actions from a finite set. Working under the assumption that the system under consideration is passive and large-time norm observable, we propose a static feedback mapping, from the output space to the finite set of control actions, which is shown to be practically stabilizing if the convex hull of certain control actions (in the chosen finite set) contains the origin in its interior. Consequently, to construct this stabilizing feedback, it suffices to have, in addition to a zero symbol, another m + 1 elements in the control set which form an m-simplex in R m (the input, and output space).

We study the asymptotic stability of Lur'e systems with butterfly hysteresis nonlinearities modeled by the Preisach operators with respect to a set of equilibrium points. We present the input-output rate property of the Preisach operators that exhibit butterfly hysteresis behavior. Based on this characterization, we present sufficient conditions on the linear systems that guarantee the asymptotic stability of the closed-loop system to a set of equilibrium points via circle criterion. Finally numerical simulations are presented to demonstrate these results.

International audience; Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turn, is also equivalent to the existence of a symmetric covariant tensor field, which satisfies a Control Matrix Function inequality. Based on this result, we provide the construction of such synchronizer via backstepping approaches. In some particular cases, we show how global exponential synchronization may be obtained.

In this paper, we propose a trajectory tracking controller for fully-actuated port-Hamiltonian (pH) mechanical systems, which is based on recent advances in contraction analysis and differential Lyapunov theory. The tracking problem is solved by defining a suitable invariant sliding manifold which provides a desired steady state behavior. The manifold is then made attractive via contraction techniques. Finally, we present numerical simulation results where a SCARA robot is commanded by the proposed tracking control law.

This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the appealing properties of the popular distance-based rigid formation control, but with the additional advantage of requiring the control of fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the controlled formation in order to steer the formation as a whole with translations and rotations in a prescribed way. We provide both theoretical analysis and illustrative simulations.

We study a containment control problem (CCP) and a shape control problem (SCP) for systems whose initial condition is a random variable with known distribution. The two control problems both require exponential convergence to a desired trajectory, which is complemented by either; i) a required cumulative distribution over a prescribed containment set at a specific transient time for the CCP, or; ii) a maximum distance between an attained and a desired probability density function of the state for the SCP. For the CCP, we obtain solutions for both linear and nonlinear systems by designing the closed-loop such that the initial pdf shrinks or contracts to a desired trajectory. For the SCP, we obtain solutions for linear systems and an admissible desired pdf, by designing the closed-loop such that the evolution of the pdf at the transient time is similar to the target pdf.

International audience; We investigate how the following properties are related to each other: i)-A manifold is " transversally " exponentially stable; ii)-The " transverse " linearization along any solution in the manifold is exponentially stable; iii)-There exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property.

Control engineering (in the broad sense of the term) has become an important enabling technology in many areas of medicine. Prominent examples include the artificial pancreas, closed-loop anesthesia, and personalized drug dosing strategies in neurology, oncology, endocrinology, and psychiatry. It is a testament to the power of control systems that allow individualizing treatment by providing mechanisms for linking treatment goals to treatment regimens, thus achieving a desired therapeutic effect. Consequently, the arrival of control systems engineering to the clinic enables the visionary concept of "treat the patient, not the disease" technologically and economically feasible.

This paper presents a robustness analysis of gradient-based formation control law for second-order agents subjected to distance mismatches or constant disturbances. It is shown that, akin to the first-order case, the existence of these mismatches introduces two undesired group behaviors: a distorted final shape and a stationary group motion. We show that such undesired properties can be compensated by combining the gradient-based rigid formation control law and our proposed distributed estimators.

A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in chemical reaction network theory, and which directly relates to the thermodynamics of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This directly leads to the characterization of the set of equilibria and their stability. Both the form of the dynamics and the deduced dynamical behavior are very similar to consensus dynamics. The assumption of complex-balancedness is revisited from the point of view of Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using the classical idea of extending the graph of chemical complexes by an extra 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action outflows is given., Comment: 18 pages

Despite the great success of using gradient-based controllers to stabilize rigid formations of autonomous agents in the past years, surprising yet intriguing undesirable collective motions have been reported recently when inconsistent measurements are used in the agents' local controllers. To make the existing gradient control robust against such measurement inconsistency, we exploit local estimators following the well known internal model principle for robust output regulation control. The new estimator-based gradient control is still distributed in nature and can be constructed systematically even when the number of agents in a rigid formation grows. We prove rigorously that the proposed control is able to guarantee exponential convergence and then demonstrate through robotic experiments and computer simulations that the reported inconsistency-induced orbits of collective movements are effectively eliminated., 10 pages

In this paper, we study a Passivity-Based Control (PBC) design that solves asymptotic stability with guaranteed safety problem via Interconnection and Damping Assignment (IDA) approach. Akin to the classical IDA-PBC method, the original system is transformed via a state-feedback to a port-Hamiltonian system where the corresponding interconnection and damping matrices and the energy function are shaped according to the given set of unsafe states and to the desired equilibrium point. By embedding it in a hybrid control framework, we show how the global results can also be obtained. We illustrate the efficacy of our proposed method on a nonlinear second-order system.

The role of the internal model principle is investigated in this paper for the coordination of relative-degree-one and relative-degree-two nonlinear systems. For relative-degree-one systems that are incrementally (output-feedback) passive, we propose internal-model-based distributed control laws which guarantee output synchronization to an invariant manifold driven by autonomous synchronized internal models. For relative-degree-two systems, we consider a different internal-model-based distributed control framework for solving a formation control problem where the agents have to track a reference signal available only to the leader agent. In both cases, the local controller is also able to reject the disturbance signals generated by a local exosystem.

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input–output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation., 14 pages, conditionally accepted in Automatic Control, IEEE Transactions on

Recently it has been reported that range-measurement inconsistency, or equivalently mismatches in prescribed inter-agent distances, may prevent the popular gradient controllers from guiding rigid formations of mobile agents to converge to their desired shape, and even worse from standing still at any location. In this paper, instead of treating mismatches as the source of ill performance, we take them as design parameters and show that by introducing such a pair of parameters per distance constraint, distributed controller achieving simultaneously both formation and motion control can be designed that not only encompasses the popular gradient control, but more importantly allows us to achieve constant collective translation, rotation or their combination while guaranteeing asymptotically no distortion in the formation shape occurs. Such motion control results are then applied to (a) the alignment of formations orientations and (b) enclosing and tracking a moving target. Besides rigorous mathematical proof, experiments using mobile robots are demonstrated to show the satisfying performances of the proposed formation-motion distributed controller., Comment: 14 pages

We propose a novel nonlinear control method for solving the problem of stabilization with guaranteed safety for nonlinear systems. The design is based on the merging of the well-known Control Lyapunov Function (CLF) and the recent concept of Control Barrier Function (CBF). The proposed control method allows us to combine the design of a stabilizing feedback law based on CLF and the design of safety control based on CBF(s); both of which can be designed independently. Our proposed approach can also accommodate the case of multiple CBFs which correspond to multiple different sets of unsafe states. Lastly, the efficacy of the proposed approach is demonstrated in the simulation results on the stabilization of a nonlinear mechanical system and on the navigation of a mobile robot.

Recent technological advances in molecular biology have enabled not only the real-time measurement of molecular activities in cellular systems but also the ability to manipulate some of these through engineered molecular-actuation systems and the ability to design new cellular systems that do not yet exist in nature. These capabilities have expanded the field of systems biology, which originally aimed at providing new biological insights or unravelling mechanisms through a systems perspective. Now the aim of the field, known as synthetic biology, is to design novel cellular systems that are regulated through engineered control systems. This field has been put into the mainstream by the annual International Genetically Engineered Machine (iGEM) competition.

This paper discusses the cryogenic mechatronic development of the Focal Plane Chopper (FPC) mechanism in the Heterodyne Instrument for the Far Infrared (HIFI) which is one of the science instruments on board the Herschel space telescope. The extreme cryogenic environment, in which the mechanism has to operate, places a number of constraints on the mechatronic design of the instrument. The paper gives an overview of cryogenic design issues applicable to the development of the FPC and provides solutions to the problems encountered. (C) 2011 Elsevier Ltd. All rights reserved.

This article provides an overview of the circle criterion and its connection with ISS. Classical absolute stability theory and the circle criterion in particular, is concerned with the analysis of a feedback interconnection of Lure type, which consists of a linear system in the forward path and a sector-bounded nonlinearity in the negative feedback path. Classical absolute stability results are revis ited in the context of systems described by differential inclusions and within a framework based on the complex Aizerman conjecture. Contrast with the classical literature that is focused mainly on asymptotic stability of the feedback interconnection, ISS issues are addressed and resolved.

We show that the state of a strictly output passive system with an L(2) input converges to zero. The result is applied to the disturbance rejection problem (with reference signal zero), where the disturbance can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an L(2) signal. Using an LTI controller, constructed based on the internal model principle, the state trajectories of the plant (and hence also the error signal) converge to zero.

The efficacy of proportional, integral and derivative (PID) control for set point regulation and disturbance rejection is investigated in a context of second-order systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the restoring force action of the system ('hysteretic spring' effects); in the second, the hysteretic component resides (externally) in the input channel (e.g. piezo-electric actuators). In each case, robust conditions on the PID gains, explicitly formulated in terms of the system data, are determined under which asymptotic tracking of constant reference signals and rejection of constant disturbance signals is guaranteed. Keywords: hysteresis; non-linear systems; PID control; tuning regulators

We present the main results of the performance test campaign of the Mid-Infrared European Extremely Large Telescope Imager and Spectrograph (METIS) Cold Chopper Demonstrator (MCCD). This tip/tilt mirror, which operates at a temperature of 77 K, is one of the critical components in the METIS for the European Extremely Large Telescope. The performance requirements of the MCCD relate to the field of fast and very accurate reference tracking. We discuss the applicability of different high-performance motion control strategies and describe the control synthesis of a repetitive and of a novel hybrid controller. We identified the presence of nonlinearities in the plant, which limits the performance of the hybrid controller. The repetitive controller shows very promising results and can handle the nonlinearities in the system. This experimental phase concludes the MCCD program, which was initiated to verify the feasibility of a high-performance cryogenic tip/tilt mirror at an early stage in the METIS development. Because of the very promising test results, no significant changes to the hardware will be implemented. We believe that minor adjustments will suffice to meet all requirements of the final hardware after integration with the METIS instrument.

In this technical note, we revisit a control design approach for general (non-affine) nonlinear systems using relaxed control. Using the notion of relaxed input, where the ordinary real-valued control input is replaced by a measure-valued control input, we are able to manipulate the original system such that the resulting relaxed system is amenable to control. We show the applicability of using relaxed input for transforming a non-affine nonlinear system into an affine one such that the relaxed system has desirable control properties. Finally, we present a practical implementation of relaxed input via ordinary control input which is based on the sampled-data of the relaxed input.

In this paper, the robust coordination of multi-agent systems via energy-shaping is studied. The agents are nonidentical, Euler-Lagrange systems with uncertain parameters which are regulated (with and without exchange of information between the agents) by the classical energy-based controller where the potential energy function is shaped such that, if the parameters are known, all agents converge globally to the same desired constant equilibrium. Under parameter uncertainty, the globally asymptotically stable (GAS) equilibrium point is shifted away from its desired value and this paper shows that adding information exchange between the agents to the decentralized control policy improves the steady-state performance. More precisely, it proves that if the undirected communication graph is connected, the equilibrium of the networked controller is always closer (in a suitable metric) to the desired one than that of the decentralized controller. The result holds for all interconnection gains if the potential energy functions are quadratic, else, it is true for sufficiently large gains. An additional advantage of networking is that the asymptotic stabilization objective can be achieved by using lower gains into the loop. Some experimental results (using two nonlinear manipulators) given support to the main results of the paper. (C) 2013 Elsevier Ltd. All rights reserved.

In this paper we investigate the dissipativity property of a certain class of Duhem hysteresis operator, which has clockwise (CW) input-output (I/O) behavior. In particular, we provide sufficient conditions on the Duhem operator such that it is CW and propose an explicit construction of the corresponding storage function satisfying dissipation inequality of CW systems. The result is used to analyze the stability of a second order system with hysteretic friction which is described by a Dahl model., Pre-print, revised manuscript, 19 pages

In this paper, we discuss the dissipativity property of the counterclockwise Duhem operator. Sufficient conditions on the functions which define the Duhem operator are given such that the Duhem operator has counterclockwise input-output dynamics. In particular, an explicit construction of the storage functions satisfying the counterclockwise dissipation inequality is given. The constructed storage function is also related to the underlying anhysteresis function which is commonly used to describe hysteresis in magnetic materials. The results can thus facilitate analysis of systems with the counterclockwise Duhem operator via the dissipativity approach. (C) 2012 Elsevier Ltd. All rights reserved.

For a class of dissipative nonlinear systems, it is shown that an iISS (integral input-to-state stability) gain can be computed directly from the corresponding supply function. The result is used to prove the convergence to zero of the state whenever the input signal has bounded energy, where the energy functional is determined by the supply function.