Showing papers by "Wpmh Maurice Heemels published in 2010"

Output-based event-triggered control with Guaranteed ℒ ∞ -gain and improved event-triggering

Abstract: Most event-triggered controllers available nowadays are based on static state-feedback controllers. As in many control applications the full state is not available for feedback, it is the objective of this paper to propose event-triggered dynamical output-based controllers. The fact that the controller is based on output feedback instead of state feedback does not allow for straightforward extensions of existing event-triggering mechanisms if a minimum time between two subsequent events, the so-called ‘minimum inter-event time’, has to be guaranteed. Therefore, we will propose an event-triggering mechanism that invokes execution of the control task when the difference between the measured output or the control input of the plant or controller, respectively, and its previously sampled value becomes ‘large’ compared to its current value and an additional threshold. For such event-triggering mechanisms, we will study closed-loop stability and ℒ ∞ -performance and provide bounds on the minimum inter-event time. In addition, we will model the event-triggered control system using impulsive systems, which truly describe the behaviour of the event-triggered control system. As a result, we can guarantee stability and performance for improved event-triggered controllers with larger minimum inter-event times than existing results in literature.

Observer-Based Control of Discrete-Time LPV Systems With Uncertain Parameters $ $

Abstract: In this note, linear matrix inequality-based design conditions are presented for observer-based controllers that stabilize discrete-time linear parameter-varying systems in the situation where the parameters are not exactly known, but are only available with a finite accuracy. The presented framework allows to make tradeoffs between the admissible level of parameter uncertainty on the one hand and the transient performance on the other. In addition, the level of parameter uncertainty can be maximized while still guaranteeing closed-loop stability.

Performance analysis of reset control systems

Abstract: In this paper we present a general linear matrix inequality-based analysis method to determine the performance of a SISO reset control system in both the ℒ2 gain and ℋ2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ2 gain performance and the ℋ2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear-based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ℒ2 gain and ℋ2 norm calculations and show that, for an input constrained ℋ2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.

Comparison of overapproximation methods for stability analysis of networked control systems

Abstract: The presence of a communication network in a control loop induces many imperfections such as varying transmission delays, varying sampling/transmission intervals and packet loss, which can degrade the control performance significantly and can even lead to instability. Various techniques have been proposed in the literature for stability analysis and controller design for these so-called networked control systems (NCSs). The goal of this paper is to survey a particular class of techniques using discrete-time models that are based on polytopic overapproximations of the uncertain NCS model and lead to stability conditions in terms of linear matrix inequalities (LMIs). We discuss the advantages and disadvantages of the existing techniques in both qualitative and quantitative manners. In particular, we apply all methods to a benchmark example providing a numerical comparison of the methods with respect to conservatism as well as numerical complexity.

Stability and stabilization of networked control systems

Abstract: The presence of a communication network in a control loop induces many imperfections such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects, which can degrade the control performance significantly and even lead to instability. Various techniques have been proposed in the literature for stability analysis and controller design for these so-called networked control systems. The aim of this chapter is to survey the main research lines in a comprehensive manner.

Stability analysis of stochastic Networked Control Systems

Abstract: In this paper, we study the stability of Networked Control Systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, packet-dropouts and communication constraints. Communication constraints impose that, per transmission, only one sensor or actuator node can access the network and send its information. Which node is given access to the network at a transmission time is orchestrated by a so-called network protocol. This paper considers NCSs, in which the transmission intervals and transmission delays are described by a random process, having a continuous probability density function (PDF). By focussing on linear plants and controllers and periodic and quadratic protocols, we present a modelling framework for NCSs based on stochastic discrete-time switched linear systems. Stability (in the mean-square) of these systems is analysed using convex overapproximations and a finite number of linear matrix inequalities. On a benchmark example of a batch reactor, we illustrated the effectiveness of the developed theory.

Stability analysis and controller synthesis for hybrid dynamical systems

Abstract: Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

On integration of event-based estimation and robust MPC in a feedback loop

Abstract: The main purpose of event-based control, if compared to periodic control, is to minimize data transfer or processing power in networked control systems. Current methods have an (implicit) dependency between triggering the events and the control algorithm. To decouple these two, we introduce an event-based state estimator in between the sensor and the controller. The event-based estimator is used to obtain a state estimate with a bounded covariance matrix in the estimation error at every synchronous time instant, under the assumption that the set in the measurement-space that is used for event generation is bounded. The estimation error is then translated into explicit polytopic bounds that are fed into a robust MPC algorithm. We prove that the resulting MPC closed-loop system is input-to-state stable (ISS) to the estimation error. Moreover, whenever the network requirements are satisfied, the controller could explicitly request for an additional measurement in case there is a desire for a better disturbance rejection.

Disturbance decoupling of switched linear systems

Abstract: In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the continuous exogenous input is considered as the disturbance, in the second the switching signal and in the third both of them are considered as disturbances. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.

A Model Predictive Control Approach to Design a Parameterized Adaptive Cruise Control

Abstract: The combination of different desirable characteristics and situation-dependent behavior cause the design of adaptive cruise control (ACC) systems to be time consuming and tedious. This chapter presents a systematic approach for the design and tuning of an ACC, based on model predictive control (MPC). A unique feature of the synthesized ACC is its parameterization in terms of the key characteristics safety, comfort and fuel economy. This makes it easy and intuitive to tune, even for nonexperts in (MPC) control, such as the driver. The effectiveness of the design approach is demonstrated using simulations for some relevant traffic scenarios.

On dropout modelling for stability analysis of networked control systems

Abstract: This paper presents three discrete-time modelling approaches for networked control systems (NCSs) that incorporate time-varying sampling intervals, time-varying delays and dropouts The focus of this work is on the extension of two existing techniques to describe dropouts, namely (i) dropouts modelled as prolongation of the delay and (ii) dropouts modelled as prolongation of the sampling interval, and the presentation of a new approach (iii) based on explicit dropout modelling using automata Based on polytopic overapproximations of the resulting discrete-time NCS models, we provide LMI-based stability conditions for all three approaches Herewith, we compare the extensions of the existing approaches and the newly proposed method in terms of modelling accuracy, conservatism and complexity of the stability analysis Using an illustrative example, we provide a thorough numerical comparison of the alternative modelling approaches

Reference Governors for Controlled Belt Restraint Systems

Abstract: Today's restraint systems typically include a number of airbags, and a three-point seat belt with load limiter and pretensioner. For the class of real-time controlled restraint systems, the restraint actuator settings are continuously manipulated during the crash. This paper presents a novel control strategy for these systems. The control strategy developed here is based on a combination of model predictive control and reference management, in which a non-linear device - a reference governor (RG) - is added to a primal closed-loop controlled system. This RG determines an optimal setpoint in terms of injury reduction and constraint satisfaction by solving a constrained optimisation problem. Prediction of the vehicle motion, required to predict future constraint violation, is included in the design and is based on past crash data, using linear regression techniques. Simulation results with MADYMO models show that, with ideal sensors and actuators, a significant reduction (45%) of the peak chest acceleration can be achieved, without prior knowledge of the crash. Furthermore, it is shown that the algorithms are sufficiently fast to be implemented online.

Stability analysis of networked control systems: A sum of squares approach

Abstract: This paper presents a sum of squares (SOS) approach to the stability analysis of networked control systems (NCSs) incorporating time-varying delays and time-varying transmission intervals. We will provide mathematical models that describe these NCSs and transform them into suitable hybrid systems formulations. Based on these hybrid systems formulations we construct Lyapunov functions using SOS techniques that can be solved using LMI-based computations. This leads to several advantages: (i) we can deal with nonlinear polynomial controllers and systems, (ii) we can allow for nonzero lower bounds on the delays and transmission intervals in contrast with various existing approaches, (iii) we allow more flexibility in the Lyapunov functions thereby possibly obtaining improved bounds for the delays and transmission intervals than existing results, and finally (iv) it provides an automated method to address stability analysis problems in NCS.

Stability analysis for nonlinear Networked Control Systems: A discrete-time approach

Abstract: In this paper we develop a framework for the stabilising controller design for nonlinear Networked Control Systems (NCSs) with time-varying sampling intervals, time-varying delays and packet dropouts. As opposed to emulation-based approaches where the effects of sampling-and-hold and delays are ignored in the phase of controller design, we propose an approach in which the controller design is based on approximate discrete-time models constructed for a nominal (non-zero) sampling interval and a nominal delay while taking into account sampling-and-hold effects. Subsequently, sufficient conditions for the global exponential stability of the closed-loop NCS are provided. The results are illustrated by means of an example.

An approach to observer-based decentralized control under periodic protocols

Abstract: This paper provides an approach to analyze and design decentralized observer-based controllers for large-scale linear plants subject to network communication constraints and varying sampling intervals. Due to communication constraints, it is impossible to transmit all input and output data simultaneously over the communication network that connects sensors, actuators and controllers. A protocol orchestrates what data is sent over the network at each transmission instant. To handle these communication constraints, it is fruitful to adopt a switched observer structure that switches based on the transmitted information. By taking a discrete-time switched linear system perspective, we are able to derive a general model that captures all these aspects and provides insight into how they influence each other. Focusing on the class of so-called ‘periodic protocols ’ (of which the well-known Round Robin protocol is a special case), we provide a method to assess robust stability using a polytopic overapproximation and LMI-based stability conditions. Although the design problem is in general non-convex, we provide a procedure to find stabilizing control laws by simplifying the control problem. The design of the controller exploits the periodicity of protocols and ignores the global coupling between subsystems of the plant and variation of the sampling intervals. To assess the robust stability of the resulting closed-loop system including the ignored effects, an a posteriori analysis is conducted based on the derived LMIs.

On the synthesis of piecewise affine control laws

Abstract: Piecewise affine (PWA) control laws offer an attractive solution to real-time control of linear, nonlinear and hybrid systems. In this paper we provide a compact exposition of the existing state-of-the-art methods for the synthesis of PWA control laws using optimization-based methods.

A Disturbance Attenuation Approach for a Class of Continuous Piecewise Affine Systems: Control Design and Experiments

Abstract: We consider the disturbance attenuation problem for a class of continuous piecewise affine systems. Hereto, observer-based output-feedback controllers are proposed that render the closed-loop system uniformly convergent. The convergence property ensures, first, stability and, second, the existence of a unique, bounded, globally asymptotically stable steady-state solution for each bounded disturbance. The latter property is key in uniquely specifying closed-loop performance in terms of disturbance attenuation. Because of its importance in engineering practice, the class of harmonic disturbances is studied in particular and performance measures for this class of disturbances are proposed based on so-called generalized frequency response functions for convergent systems. Additionally, the derived control strategy is extended by including conditions that guarantee the satisfaction of a bound on the control input. The effectiveness of the proposed control design strategy is illustrated by the application of the results to an experimental benchmark system being a piecewise affine beam system.

edited by) Networked Control Systems

Abstract: There has been a recent surge in research activities related to networked control of large-scale systems. These "cyber-physical" systems can be found throughout society, from industrial production plants, to water and energy distribution networks and transportation systems. They are characterized by tight coordination of a pervasive sensing infrastructure, distributed computing elements, and the physical world. Developed from work presented at the 3rd WIDE PhD School on Networked Control Systems held in Siena in July 2009, Networked Control Systems contains tutorial introductions to key research topics in the area of networked control.

Convergence of discrete-time approximations of constrained linear-quadratic optimal control problems

Abstract: Continuous-time linear constrained optimal control problems are in practice often solved using discretization techniques, e.g. in model predictive control (MPC). This requires the discretization of the (linear time-invariant) dynamics and the cost functional leading to discrete-time optimization problems. Although the question of convergence of the sequence of optimal controls, obtained by solving the discretized problems, to the true optimal continuous-time control signal when the discretization parameter (the sampling interval) approaches zero has been addressed in the literature, we provide some new results under less restrictive assumptions for a class of constrained continuous-time linear quadratic (LQ) problems with mixed state-control constraints by exploiting results from mathematical programming extensively. As a byproduct of our analysis, a regularity result regarding the costate trajectory is also presented.