Hybrid Control Systems : An Introductory Discussion to the Special Issue

This introductory paper provides an overview of hybrid systems and gives a brief introduction to the major approaches in hybrid systems research with several book references. A brief guide for the papers in this special issue, which present several approaches to modeling, analysis, and synthesis of hybrid systems, is also given. I. THE HYBRID NATURE OF HYBRID SYSTEMS H YBRID means, in general, heterogeneous in nature or composition. The term hybrid systems is understood to mean systems with behavior defined by entities or processes of distinct characteristics. The hybrid systems of interest here are dynamic systems where the behavior of interest is determined by interacting continuous and discrete dynamics. These systems typically contain variables or signals that take values from a continuous set (e.g., the set of real numbers) and also variables that take values from a discrete, typically finite set (e.g., the set of symbols ). These continuous or discrete-valued variables or signals depend on independent variables such as time, which may also be continuous or discrete; some of the variables may also be discrete-event driven in an asynchronous manner. There are many examples of hybrid systems. In the control area, a very well-known instance of a hybrid system is when a continuous-time linear time-invariant plant described by linear differential equations (which involve continuousvalued variables that depend on continuous time) is controlled by a discrete-time linear time-invariant plant described by linear difference equations (which involve continuous-valued variables that depend on discrete time). These types of systems are typically studied in courses under the name of sampleddata systems or digital control systems; digital control systems may of course include more general types of systems such as time-varying and nonlinear plants and controllers. If one also considers quantization of the continuous-valued variables or signals, then the hybrid systems contain not only continuousvalued variables that are driven by continuous and discrete times, but also discrete-valued signals as well. Note that recent studies of digital control systems in the hybrid systems literature typically involve nonlinear plants and controllers. Another familiar example of a hybrid control system is a switching system where the dynamic behavior of interest can be adequately described by a finite (small) number of dynamical models, that are typically sets of differential or difference equations, together with a set of rules for switching among these models. These switching rules are described by Publisher Item Identifier S 0018-9286(98)02657-9. logic expressions or a discrete-event system with a finite automaton or a Petri net representation. Another existing area that has been brought recently under the hybrid systems framework is the study of properties (e.g., stability) of dynamical systems described by differential equations with discontinuities present. A familiar simple example of a practical hybrid control system is the heating and cooling system of a typical home. The furnace and air conditioner, along with the heat flow characteristics of the home, form a continuous-time system which is to be controlled. The thermostat is a simple asynchronous discrete-event driven system which basically handles the symbols {too hot, too cold} and {normal}. The temperature of the room is translated into these representations in the thermostat and the thermostat’s response is translated back to electrical currents which control the furnace, air conditioner,