Control Using Logic and Switching

Tutorial workshop for the

40th IEEE Conference on Decision and Control

December 4-7, 2001, in Orlando, Florida

The overall objective of this tutorial workshop is to overview a variety of 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. The overall models of systems composed of such logics together with the processes they are intended to control, are concrete examples of what might be called “hybrid dynamical systems.”

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 re-configurable systems, fault correction systems, and certain types of parameter-adaptive systems. Major reasons for introducing logic and switching are to deal with communication, actuator and sensor constraints, with model uncertainty, with unforeseen events or to avoid performing difficult tasks e.g., precise equipment calibration which might otherwise be necessary were one to consider only conventional controls.

The aim of this workshop is to provide an overview of algorithms with these capabilities, as well as to discuss various techniques for analyzing the types of switched systems that result.

Organizers

João Hespanha University of California at Santa Barbara Room 3121, Engineering I Electrical & Computer Eng. University of California Santa Barbara, CA 93106 USA Tel: +1 (805) 893-7042 Fax: +1 (805) 893-3262 hespanha at ece.ucsb.edu

Daniel Liberzon University of Illinois at Urbana-Champaign Coordinated Science Laboratory Univ. of Illinois 1308 W. Main Street Urbana, IL 61801 USA Tel: +1 (217) 244-6750 Fax: +1 (217) 244-1653 liberzon at uiuc.edu

A. Stephen Morse Yale University Dept. of Electrical Engineering PO Box 208267 Yale University New Haven, CT 06520 USA Tel: +1 (203) 432-4295 Fax: +1 (203) 432-7481 morse at sysc.eng.yale.edu

Program

Part I – Switched Systems (Liberzon)

08:00 – 08:45 Switched Control Systems

08:45 – 10:15 Stability of Switched Systems

These two lectures were based on the manuscript:

Daniel Liberzon, Control using Logic and Switching, Dec 2001.

Part II – Self-Adjusting Control (Morse)

10:30 – 12:00 Framework for Self-Adjusting Control

01:00 – 02:15 Achieving Detectability

These two lectures were based on the manuscript:

A. Stephen Morse, Notes on Self-Adjusting Control Systems, Dec 2001.

Part III – Supervisory Control (Hespanha)

02:15 – 03:45 Supervisory Control of Families of Linear Controllers

03:45 – 05:15 Supervisory Control of Families of Nonlinear Controllers

These two lectures were based on the manuscript:

João Hespanha, Tutorial on Supervisory Control, Nov. 2001.

You can download the slides used in Part III from here.