Showing papers by "Wpmh Maurice Heemels published in 2009"

Stability of Networked Control Systems With Uncertain Time-Varying Delays

Abstract: In this technical note, a new approach for the stability analysis and controller synthesis of networked control systems (NCSs) with uncertain, time-varying, network delays is presented. Based on the Jordan form of the continuous-time plant, a discrete-time representation of the NCS is derived. Using this model for delays that can be both smaller and larger than the sampling interval, sufficient LMI conditions for stability and feedback stabilization are proposed. The results are illustrated by a typical motion control example.

Observer Design for Lur'e Systems With Multivalued Mappings: A Passivity Approach

Abstract: This paper considers the design of state observers for Lur'e systems with multivalued mappings in the feedback path. In particular, we focus on maximal monotone mappings that that do not require any compactness and local boundedness properties and include various models for relays, friction characteristics and complementarity conditions. We propose two types of observers that are constructed by rendering a suitable operator passive in an appropriate sense. The well-posedness properties of the observer dynamics are carefully analyzed and the global asymptotic stability of the observation error is formally proven.

Introduction to hybrid systems

Abstract: This chapter gives an informal introduction to hybrid dynamical systems and illlustrates by simple examples the main phenomena that are encountered due to the interaction of continuous and discrete dynamics. References to numerous applications show the practical importance of hybrid systems theory.

and Input-to-State Stability Subtleties for Discrete-time Discontinuous Systems

Abstract: In this note we consider stability analysis of discrete-time discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov is precar- ious for discrete-time discontinuous dynamics. Also, we indicate that a particular type of Lyapunov condition, slightly stronger than the classical one, is required to establish stability of discrete-time discontinuous systems. Furthermore, we examine the robustness of the stability property when it was attained via a discontinuous Lyapunov function, which is often the case for discrete-time hybrid systems. In contrast to existing results based on smooth Lyapunov functions, we develop several input- to-state stability tests that explicitly employ an available discontinuous Lyapunov function. Index Terms—Discrete-time, Discontinuous systems, Stability, Input- to-state stability, Lyapunov methods.

Lyapunov Functions, Stability and Input-to-State Stability Subtleties for Discrete-Time Discontinuous Systems

Abstract: In this note we consider stability analysis of discrete-time discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov is precarious for discrete-time discontinuous dynamics. Also, we indicate that a particular type of Lyapunov condition, slightly stronger than the classical one, is required to establish stability of discrete-time discontinuous systems. Furthermore, we examine the robustness of the stability property when it was attained via a discontinuous Lyapunov function, which is often the case for discrete-time hybrid systems. In contrast to existing results based on smooth Lyapunov functions, we develop several input-to-state stability tests that explicitly employ an available discontinuous Lyapunov function.

Networked and quantized control systems with communication delays

Abstract: There are many communication imperfections in networked control systems (NCSs) such as varying sampling/transmission intervals, varying delays, possible packet loss, communication constraints and quantization effects. Most of the available literature on NCSs focuses on only some of these phenomena, while ignoring the others, although recently some papers appeared that consider at least three of these phenomena. In one paper time-varying delays, time-varying transmission intervals and communication constraints are considered, while in an other time-varying transmission intervals, communication constraints and quantization effects are studied. As both approaches are based on the same underlying hybrid modeling framework, it will be shown here that the models can be combined in a unifying hybrid model including the five mentioned network phenomena under some restrictions. On the basis of this model, stability will be analyzed of the closed-loop system in which the controller is obtained using an emulation approach. The analysis provides tradeoffs between the maximally allowable transmission interval (MATI), the maximally allowable delay (MAD) and the quantization parameters, while still guaranteeing closed-loop stability.

Survey of modeling, analysis, and control of hybrid systems

Abstract: An overview of various modeling frameworks for hybrid systems is given followed by a comparison of the modeling power and the model complexity, which can serve as a guideline for choosing the right model for a given analysis or control problem with hybrid dynamics. Then, the main analydsis and design tasks for hybrid system.s are surveyed together with the methods for their solution, which will be discussed in more detail in subsequent chapters.

Networked control systems with communication constraints: Tradeoffs between transmission intervals and delays

Abstract: There are many communication imperfections in networked control systems (NCSs) such as varying delays, varying transmission intervals, packet loss, communication constraints and quantization effects Most of the available literature on NCSs focuses on only one of these aspects, while ignoring the others In this paper we present a general framework that incorporates both communication constraints (only one node accessing the network per transmission), varying delays and varying transmission intervals Based on a newly developed NCS model including these three network phenomena, we will provide an explicit (Lyapunov-based) procedure to compute bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS The developed results lead to tradeoff curves between MATI and MAD as will be illustrated using a benchmark example

Decoupling-based reconfigurable control of linear systems after actuator faults

Abstract: In this paper, we provide the complete solution to the reconfigurable control problem after actuator faults in linear dynamical systems by means of disturbance decoupling approaches. The recovery of the closed-loop internal stability and the exact and approximate recovery of nominal tracking and performance are our main reconfiguration goals. We state necessary and sufficient conditions for the solvability of these problems. The approximate approach broadens the scope of potential applications. A thermofluid process is used to illustrate the exact and approximate methods.

Comparison of stability characterisations for networked control systems

Abstract: This paper presents linear matrix inequalities for stability analysis for networked control systems (NCSs) that incorporates various network phenomena: time-varying sampling intervals, packet dropouts and time-varying delays that may be both smaller and larger than the sampling interval. The problem is approached from a discrete-time modelling perspective. A comparison is made between the use of Parameter Dependent Lyapunov functions and Lyapunov-Krasovskii functions for stability analysis. Examples illustrate the developed theory.

Design of observer-based controllers for LPV systems with unknown parameters

Abstract: Output-based feedback control of LPV systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. In this paper we consider this problem in the case of discrete-time LPV systems for which the parameters are not exactly known, but only available with a finite accuracy or affected by noise during their measurement. The controllers are obtained using a separate design of an observer and a state feedback and the interconnection is proven to stabilize the LPV system despite the mismatch between the true and available parameters. The approach allows to maximize the parameter uncertainty while still guaranteeing closed-loop stability. In addition, it is possible to make tradeoffs between the admissible level of mismatch on the one hand and the performance in terms of decay factors on the other. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example.

Further Results on "Robust MPC Using Linear Matrix Inequalities"

Abstract: This paper presents a novelmethod for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and \(\mathcal{H}_\infty\) control design. This relation shows that the LMI-based optimal solution of the \(\mathcal{H}_\infty\) synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.

Self-optimizing Robust Nonlinear Model Predictive Control

Abstract: This paper presents a novel method for designing robust MPC schemes that are self-optimizing in terms of disturbance attenuation. The method employs convex control Lyapunov functions and disturbance bounds to optimize robustness of the closed-loop system on-line, at each sampling instant - a unique feature in MPC. Moreover, the proposed MPC algorithm is computationally efficient for nonlinear systems that are affine in the control input and it allows for a decentralized implementation.

Further switched systems

Abstract: Mixed logical dynamical systems and linear complementarity systems are representations of switched systems, which under the conditions described here are equivalent to the model used in Chapter 4. They are particularly useful for model-predictive control. The equivalences of several hybrid system models show that different models, which are suitable for specific analysis and design problems and have been investigated in detail, cover the same class of hybrid systems. The analysis of the well-posedness of the models leads to conditions on the model equations under which a unique solution exists.

Linear control of time-domain constrained systems

Abstract: Recent results on the control of linear systems subject to time-domain constraints could only handle the case of closed-loop poles that are situated on the real axis. As most closed-loop systems in practice contain also complex poles, there is a strong need for a general framework encompassing all cases. In this paper such a framework is presented based on sums-of-squares techniques and we show indeed that time-domain constraints on closed-loop signals of linear systems can be incorporated as linear matrix inequalities, even when complex conjugate poles are assigned. The effectiveness of this complete design method is evaluated by means of a simulation example.