Switched Control Systems

Yale University, New Haven CT

Investigators

Abstract

The overall objective of this research is to develop methods for synthesizing and analyzing logic-based switching control systems. By a logic-based switching controller is meant a controller whose subsystems include not only familiar dynamical components {integrators, summers, gains, etc.} but logic-driven elements as well. An important category of such systems are those consisting of a continuous-time process to be controlled, a family of fixed-gain or variable-gain candidate controllers, and an "event-driven switching logic" called a supervisor whose job is to determine in real time which controller should be applied to the process. Examples of supervisory control systems include reconfigurable systems, fault correction systems, and certain types of parameter-adaptive systems. We propose first to refine and extend the concept of supervisory control introduced in our earlier work and second to use supervisory control as a motivating vehicle for the study of basic issues in the newly emerging field of hybrid dynamical systems. The supervisory control systems we propose to study fall in the category of adaptive control systems. Adaptive control has been under study for many years. Yet despite the numerous advances which have been made, there are major unresolved issues inhibiting the transfer of concepts into practice: Why, for example, is it still so difficult to explain to a non-expert why a particular algorithm is able to functions correctly in the face of unmodelled process dynamics and L bounded noise? How much unmodelled dynamics can a given algorithm tolerate before loop-stability is lost? How do we choose an adaptive control algorithm's many design parameters to achieve good disturbance rejection, transient response, etc.? A major goal of this research is to answer these questions-and in so doing to make adaptive control much more accessible to practitioners. We will investigate techniques enabling us to much more clearly and concisely quantify unmodelled dynamics norm bounds, disturbance-to-controlled output gains and so on. Our ultimate objective is to lay bare the ideas needed to develop a bona fide computer-aided adaptive control design methodology which relies much more on design principals then on trial and error techniques. Towards this end we will seek to derive new switching algorithms for supervisory control systems which are more amenable to analysis than those which currently exist. We will continue our study of the stability of switched dynamical systems, and we will attempt to draw conclusions about the input-output properties of such systems in terms of the input output properties of the constituant dynamical systems being switched. We will explore the connection between the stability of switched dynamical systems and the properties of the associated Lie algebras generated by the vector fields of the constituient dynamical systems being switched. We will study the problem of `covering' a continuum of candidate controllers designed so that at least one is able to regulate a process P whose uncertain model lies in an associated continuum of candidate process models M, with a finite set of candidate controllers C chosen so that for each model in M there is at least one satisfactory controller in C. Using the preceding, we will seek to develop a provably correct apporoach to supervisory control for uncertain nonlinear processes which exploits to the extent possible, established non-adaptive control design techniques and which takes into account both unmodelled dynamics and exogeneous noise.