Showing papers by "Wpmh Maurice Heemels published in 2014"
TL;DR: It is shown that for several popular event-triggering mechanisms no positive minimum inter-event time can be guaranteed in the presence of arbitrary small external disturbances or measurement noise, and it is essential to include the effects of external disturbances and measurement noise in the analysis of the computation/communication properties of event-triggered control systems.
Abstract: In this paper, we study fundamental properties of minimum inter-event times for several event-triggered control architectures, both in the absence and presence of external disturbances and/or measurement noise. This analysis reveals, amongst others, that for several popular event-triggering mechanisms no positive minimum inter-event time can be guaranteed in the presence of arbitrary small external disturbances or measurement noise. This clearly shows that it is essential to include the effects of external disturbances and measurement noise in the analysis of the computation/communication properties of event-triggered control systems. In fact, this paper also identifies event-triggering mechanisms that do exhibit these important event-separation properties.
389 citations
TL;DR: This work provides a new class of event-triggered controllers for linear systems which guarantee better quadratic performance than traditional periodic time- Triggered control using the same average transmission rate.
Abstract: Cyber-Physical Systems (CPSs) resulting from the interconnection of computational, communication, and control (cyber) devices with physical processes are wide spreading in our society. In several CPS applications it is crucial to minimize the communication burden, while still providing desirable closed-loop control properties. To this effect, a promising approach is to embrace the recently proposed event-triggered control paradigm, in which the transmission times are chosen based on well-defined events, using state information. However, few general event-triggered control methods guarantee closed-loop improvements over traditional periodic transmission strategies. Here, we provide a new class of event-triggered controllers for linear systems which guarantee better quadratic performance than traditional periodic time-triggered control using the same average transmission rate. In particular, our main results explicitly quantify the obtained performance improvements for quadratic average cost problems. The proposed controllers are inspired by rollout ideas in the context of dynamic programming.
155 citations
24 Jun 2014
TL;DR: The self-triggered controller is shown to stabilize a robust invariant set in the state space for the closed-loop system and uses constraint tightening methods as proposed in Tube Model Predictive Control to guarantee robust constraint satisfaction.
Abstract: In this paper we propose a robust self-triggered model predictive control algorithm for linear systems with additive bounded disturbances and hard constraints on the inputs and state. In self-triggered control, at every sampling instant the time until the next sampling instant is computed online based on the current state of the system. The goal is to achieve a low average sampling rate, thereby minimizing communication in the control system and possibly reducing the number of control updates as is required in sparse control applications. Naturally, and intentionally, our approach leads to long spans of time in which the plant is controlled in an open-loop fashion. Especially for unstable plants or large disturbances this necessitates taking into account the disturbance characteristics in the design of the control law in order to prevent constraint violation in the closed-loop system. We use constraint tightening methods as proposed in Tube Model Predictive Control to guarantee robust constraint satisfaction. The self-triggered controller is shown to stabilize a robust invariant set in the state space for the closed-loop system.
43 citations
TL;DR: In this paper, the problem of designing state-feedback controllers to track time-varying state trajectories that may exhibit jumps is recast as the task of asymptotically stabilizing a set, the tracking set.
Abstract: SUMMARY We study the problem of designing state-feedback controllers to track time-varying state trajectories that may exhibit jumps. Both plants and controllers considered are modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics, given in terms of a flow set, a flow map, a jump set, and a jump map. Using recently developed tools for the study of stability in hybrid systems, we recast the tracking problem as the task of asymptotically stabilizing a set, the tracking set, and derive conditions for the design of state-feedback tracking controllers with the property that the jump times of the plant coincide with those of the given reference trajectories. The resulting tracking controllers guarantee that solutions of the plant starting close to the reference trajectory stay close to it and that the difference between each solution of the controlled plant and the reference trajectory converges to zero asymptotically. Constructive conditions for tracking control design in terms of LMIs are proposed for a class of hybrid systems with linear maps and input-triggered jumps. The results are illustrated by various examples. Copyright © 2013 John Wiley & Sons, Ltd.
42 citations
01 Dec 2014
TL;DR: In this article, a dynamic event-triggered control (ETC) strategy for state-feedback systems is proposed that can simultaneously guarantee a finite ℒ p -gain from disturbance to output and a strictly positive lower bound on the inter-event times.
Abstract: In this work, a novel dynamic event-triggered control (ETC) strategy for state-feedback systems is proposed that can simultaneously guarantee a finite ℒ p -gain from disturbance to output and a strictly positive lower bound on the inter-event times (implying Zeno-freeness). The developed theory leads to tradeoff curves between (minimum and average) inter-event times and ℒ p -gains that depend on the selected medium access protocol.
37 citations
01 Jan 2014
TL;DR: A novel dynamic event-triggered control strategy for state-feedback systems is proposed that can simultaneously guarantee a finite ℒp-gain from disturbance to output and a strictly positive lower bound on the inter-event times (implying Zeno-freeness).
31 citations
01 Jan 2014
TL;DR: Using a recently developed small-gain theorem for general interconnections of hybrid systems, this paper is able to find to find a maximum allowable transmission interval and maximum allowable delay for each individual network, such that input-to-state stability of the complete NCS is guaranteed.
Abstract: In this paper we consider large-scale networked control systems (NCSs) with multiple communication networks connecting sensors, controllers and actuators. Using a recently developed smallgain theorem for general interconnections of hybrid systems, we are able to find to find a maximum allowable transmission interval (MATI) and a maximum allowable delay (MAD) for each individual network, such that input-to-state stability of the complete NCS is guaranteed.
25 citations
TL;DR: The past three decades have seen an explosive growth of the body of theoretical research in the area of networked control systems (NCSs), and the immense interest for this subject is justified by the fact that society can benefit enormously if the control community can break free from the dependence on dedicated point-to-point wiring for communication between sensors, actuators, and controllers as discussed by the authors.
Abstract: The past three decades have seen an explosive growth of the body of theoretical research in the area of networked control systems (NCSs). The immense interest for this subject is justified by the fact that society can benefit enormously if the control community can break free from the dependence on dedicated point-to-point wiring for communication between sensors, actuators, and controllers. Societal benefits can stem from several networked control application areas, which are currently being explored by researchers and engineers around the world.
21 citations
01 Dec 2014
TL;DR: This paper considers a special class of hybrid systems with periodic time-triggered jump conditions, and in which the jump map has a piecewise linear character, and presents novel conditions to do so which are significantly less conservative than the existing ones in literature.
Abstract: In this paper, we consider a special class of hybrid systems with periodic time-triggered jump conditions, and in which the jump map has a piecewise linear character. This hybrid systems class forms a relevant field of study as different control applications can be modeled in this hybrid system framework, including reset control and event-triggered control systems. After showing the unifying modeling character of this class of dynamical systems, we are interested in analyzing stability and ℒ 2 -gain properties and we present novel conditions to do so which are significantly less conservative than the existing ones in literature. The effectiveness of the proposed modeling and analysis techniques is illustrated by means of a reset control example.
12 citations
04 Jun 2014
TL;DR: The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which enables a reduction in overshoot and improves transient performance.
Abstract: In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot (i.e., improves transient performance). The resulting closed-loop dynamics can be described by a continuous-time switched dynamical system, for which we will provide sufficient conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in simulation examples.
8 citations
TL;DR: This paper forms the networked plant model as a discrete-time switched linear parameter-varying system and uses convex overapproximation techniques to arrive at a model that is amenable for controller synthesis, which yields a switched controller that is robust for the aforementioned network phenomena.
01 Dec 2014
TL;DR: This work analyzes a class of suboptimal policies for regulating the state of a switched linear system to zero while minimizing a quadratic cost and presents a numerical example illustrating the applicability of the results to event-triggered control.
Abstract: We analyze a class of suboptimal policies for regulating the state of a switched linear system to zero while minimizing a quadratic cost. Our novel results provide upper and lower bounds on the performance of instances of this class with respect to the optimal policy and other policies of interest. We present a numerical example illustrating the applicability of the results to event-triggered control.
TL;DR: It is shown that BSDP results in the best approximation of the optimal cost, when compared to existing DP methods, and that the real-time implementable solution only deviates 0.16 from the optimalcost obtained using BSDP.
01 Dec 2014
TL;DR: A class of set-valued dynamical systems that satisfy maximal monotonicity properties, which includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under certain conditions is studied.
Abstract: In this paper we study a class of set-valued dynamical systems that satisfy maximal monotonicity properties. This class includes linear relay systems, linear complementarity systems, and linear mechanical systems with dry friction under certain conditions. We discuss two numerical time-stepping schemes for the computation of periodic solutions of these systems when being periodically excited. For these two schemes we will provide formal mathematical justifications and compare them in terms of approximation accuracy and computation time using a numerical example.
24 Jun 2014
TL;DR: This paper shows that a similar analysis can be carried out for randomly sampled systems, i.e., controlled linear systems sampled at random times spaced by independent and identically distributed time-varying intervals.
Abstract: Root locus analysis is a graphical method to determine how the roots of the characteristic equation of a linear time-invariant feedback loop change with the loop gain. In this paper we show that a similar analysis can be carried out for randomly sampled systems, i.e., controlled linear systems sampled at random times spaced by independent and identically distributed time-varying intervals. For such systems, the roots of a characteristic equation determine the behavior of expected values of signals in the loop. The root locus analysis in this context is especially useful for positive systems, for which (almost sure) stability can be concluded if the roots of the characteristic equation have a negative real part, and it is particularly simple when the distribution of the intervals between sampling times is exponential or Erlang.
01 Jan 2014
TL;DR: A novel non-smooth integral controller is introduced, which aims at achieving a better transient response in terms of overshoot of a feedback controlled dynamical system.
Abstract: In this paper, we introduce a novel non-smooth integral controller, which aims at achieving a better transient response in terms of overshoot of a feedback controlled dynamical system. The resulting closed-loop system can be represented as a non-smooth system with different continuous dynamics being active in dedicated regions of the state-space. The dynamical behavior of the hybrid system will be studied through simulations.