Robust adaptive control of switched systems 41 controller switching of a. The theory of such switched systems is related to the study of hybrid systems, which has recently attracted considerable attention among control. Basic issues in this context include wellposedness, simulation, and verification. Abstractwe consider the problem of stabilizing uncertain systems with quantization. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 160861 for the advisor id. If you have additional information or corrections regarding this mathematician, please use the update form. An introduction to switching adaptive control daniel liberzon coordinated science laboratory and dept. A hybrid system is a dynamical system whose evolution depends on a coupling between variables that take values in a continuum and variables that take values in a finite or countable set 8.
A lyapunovbased smallgain theorem for interconnected switched systems. Daniel liberzon was born in the former soviet union in 1973. He is the author of the books switching in systems and control birkhauser, 2003 and calculus of variations and optimal control theory. Control and optimization, year2001, volume40, pages253269.
Daniel liberzon this textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a selfcontained resource for graduate students in engineering, applied mathematics, and related subjects. The plant uncertainty is dealt with by the supervisory adaptive control framework, which employs switching among a finite family of candidate controllers. Computation and control 2006 sayan mitra switching simulation consider two hybrid automata a and b. Stephen morse, title logicbased switching control of a nonholonomic system with parametric modeling uncertainty, journal systems control lett, year 1999, volume 38, pages 167177. Download it once and read it on your kindle device, pc, phones or tablets.
Liberzon s research interests include nonlinear control theory, analysis and synthesis of switched systems, control with limited information, and uncertain and stochastic systems. This book examines switched systems from a control theoretic perspective, focusing on stability analysis and control synthesis of systems that combine. Daniel liberzon is associate professor of electrical and computer engineering at the university of illinois, urbanachampaign. For every start state of a there is a related start state of b if x. Logicbased switching control of a nonholonomic system. Switched systems have numerous applications in control of mechanical. This article deals with inputtostate stability iss of continuoustime switched nonlinear systems. Citeseerx document details isaac councill, lee giles, pradeep teregowda. He is the author of the book switching in systems and control birkhauser, 2003 and the author or coauthor of over thirty journal articles on the above topics. In this context, the bound on the number of switching enables us to prove stability of the closedloop system in the presence of. These two tutorial lectures will address the problem of controlling systems with large modeling. Finite datarate feedback stabilization of switched and.
Classification of stable planar switched systems with two modes. Unlike most of the existing switching methods considering only estimator performance, the proposed scheme takes both estimator and controller performance into account. The slow switching condition takes the form of an upper bound on the probability mass function of the number of. Brockett, fellow, ieee abstract in this paper we describe a class of nonlinear feed.
Many researchers in systems and control theory, on the other hand, tend to regard hybrid systems as continuous systems with switching and place a greater emphasis on properties of the continuous state. Each chapter ends with a rich and useful section of notes and references. Our main resultthe smallgain theorem for interconnected switched systems with both iss and noniss subsystemsis presented and interpreted in section 3. Supervisory control supervisor process controller 1. Switching in systems and control by daniel liberzon, 9781461265740, available at book depository with free delivery worldwide. Up to four ecps can be linked together to provide control for up to 64 separate circuitsaccessories. Given a family of systems with exogenous inputs such that not all systems in the family are iss, we characterize a new and general class of switching signals under which the resulting switched system is iss. This book examines switched systems from a control theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics.
Steadystate probability distributions and optimal control daniel liberzon, member, ieee and roger w. Our overall task will be to determine what is the best control for our system. Thus, translating a hybrid system to a switched system and applying our previous result offtheshelf via. Robust adaptive switching control for markovian jump nonlinear systems via backstepping technique zhu, jin, xi, hongsheng, ling, qiang, and xie, wanqing, journal of applied mathematics, 2012 using gwas data to identify copy number variants contributing to common complex diseases zollner, sebastian and teslovich, tanya m. A lyapunovbased smallgain theorem for interconnected. Available through springerlink here subscription required. This book examines switched systems from a control theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics with switching events. He did his undergraduate studies in the department of mechanics and mathematics at moscow state university from 1989 to 1993.
Very often, optimal control problems lead to switched systems. General general power system control activities include. Switched systems and control daniel liberzon jamal. Switching in systems and control daniel liberzon the theory of switched systems is related to the study of hybrid systems, which has recently attracted considerable attention among control theorists, computer scientists, and practicing engineers. Switching in systems and controldaniel liberzon boston. An introduction to mathematical optimal control theory.
Utc institute for advanced systems engineering seminar series. Network planning and development manual network switching automatic network switching the system operator may not always be able to pre inform users about system control activities, especially in those instances when. Finitetime l1gain control for positive switched systems with timevarying delay via delta operator approach li, shuo. Methods for constructing such controller families have been discussed in the recent paper by the authors. The present paper concentrates on the switching task in a multiple model context. The bangbang funnel controller, author daniel liberzon and stephan trenn, journal49th ieee conference on decision and control. Basic problems in stability and design of switched systems ieee. We consider a control algorithm consisting of a finite family of linear controllers supervised by the hierarchical hysteresis switching logic.
As was also pointed out in 8, the current research on. The slow switching condition takes the form of an upper bound on the probability mass function of the number of switches between the initial and current time instants. Liealgebraic stability conditions for nonlinear switched. Chapter 5 addresses switching systems that arise from sensor and actuation limitations. Ergodic control of switching diffusions siam journal on. Control of switched systems with limited information. Therefore, two kinds of dynamics, namely continuous dynamics and discrete events, coexist and interact in such systems. Liealgebraic stability criteria for switched systems. He is also a fellow of the international federation of automatic control. Switching in systems and controldaniel liberzon boston, ma. This is a rough draft which may contain some errors.
Robust adaptive switching control for markovian jump nonlinear systems via backstepping technique. Liberzon, ece586, hybrid systems and control course outline online. In this case, we have direct control over the switching mechanism which can be statedependent or timedependent and may adjust it as the system evolves. He was named a fellow of the institute of electrical and electronics engineers ieee in 20 for his contributions to the analysis and design of switched, nonlinear and quantized control systems. Statedependent or timedependent autonomous or controlled details of discrete behavior are abstracted away properties of the continuous state. This book examines switched systems from a controltheoretic perspective. The objective is to sustain order and normalcy under both anticipated and unanticipated faults and disturbances. It may also serve as an introduction to this active area of research for control theorists and mathematicians. The switch position is varies periodically, such that v s t is a rectangular waveform having period t s and duty cycle d. Oct 23, 2012 switching in systems and control by daniel liberzon, 9781461265740, available at book depository with free delivery worldwide. Switching in systems and control daniel liberzon download. An introduction to switched systems fondation hadamard. Calculus of variations and optimal control theory princeton.
A switched system may be obtained from a hybrid system by neglecting the details of the discrete behavior and instead considering all possible switching patterns. Some more interesting examples where timedependent properties of dwelltime type are established a posteriori for control systems with statedependent switching can be found in hespanha and morse 1999b and liberzon and trenn 2010. Ieee transactions on automatic control, 60 12, 33963400. Comments on observability of switched linear systems. It may also serve as an introduction to this active area of research for control theorists and mathematicians, as well as a useful reference for experts in the field. A block diagram of the switching system this will provide a practical answer to the following two fundamental questions. Is it possible to switch to a better controller among the. Quantization of sensor measurements andor control signals also results in switching systems. Utc institute for advanced systems engineering seminar series dr. Submitted to systems and control letters 1 liealgebraic stability conditions for nonlinear switched systems and di. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 125768 for the advisor id. Daniel liberzon the theory of switched systems is related to the study of hybrid systems, which has gained attention from control theorists, computer scientists, and practicing engineers. His research interests include nonlinear control theory, switched and hybrid dynamical systems, control with limited information, and uncertain and stochastic systems. He is the author of switching in systems and control.
One ecp can control up to 16 separate circuitsaccessories. Ece517 lecture notes ece 517 nonlinear and adaptive. Page 209 a converse lyapunov theorem for a class of dynamical systems which undergo switching. This paper presents a new supervisory control scheme, which is based on a control relevant switching logic. Summary this book develops hardware and software architectures related to modern digital switching systems. Requiring only familiarity with the basic theory of linear systems, the book is suitable as a text for a graduate course on switched systems and switching control. This book examines switched systems from a controltheoretic perspective, focusing. For various reasons, it may be natural to apply discrete control actions, which leads to systems with controlled switching. Calculus of variations and optimal control theory a concise introduction daniel liberzon princeton princeton university press and oxford. The duty cycle is equal to the fraction of time that the switch is connected in position 1, and hence 0 d 1. Objective the objectives of power system control remains. This article surveys recent developments in three basic problems regarding stability and design of switched systems. Stephen morse y a switched system, we mean a hybrid dynamical system consisting of afamily of continuoustime subsystems and a rule that orchestrates the switching between them. Switching in systems and controls by daniel liberzon highly recommend.
An introduction to the control of switching electronic systems. Liberzon is a professor at the university of illinois at urbanachampaign. This short paper introduces the concepts of biological homeostasis and homeorhesis in decision and control of humanengineered complex systems. Is the active controller, at any time, appropriate for controlling the system. The ecp receives switching commands from the ocms, translates the commands and activates or deactivates the appropriate circuits in the boats electrical system. We study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as faulttolerant control systems, flexible manufacturing systems, etc. Switching in systems and control daniel liberzon springer. We employ an adaptive control algorithm consisting of a family of linear candidate controllers supervised by a high. Hierarchical hysteresis switching university of illinois. Liberzon editor nonlinear systems and control automatica. Switching in systems and control, birkhauser, boston, ma, jun 2003. For a static quantizer, we quantify a relationship between the quantization.