Poisson Processes and the Design of Finite State Controllers

Abstract

It is widely recognized that many of the most important challenges faced by control engineers involve the development of methods to design and analyze systems having components most naturally described by differential equations interacting with components best modeled using sequential logic. This situation can arise both in the development of high volume, cost sensitive, consumer products and in the design and certification of one of a kind, complex and expensive systems. The response of the control community to this challenge includes work on limited communication control, learning control, control languages, and various efforts on hybrid systems. This work has led to important new ideas but progress has been modest and the more interesting results seem to lack the kind of unity that would lead to a broadly inclusive theory. In this talk we describe an approach to problems of this type based on sample path descriptions of finite state Markov processes and suitable adaptations of known results about linear systems. The result is an insightful design technique yielding finite state controllers for systems governed by differential equations. We illustrate with concrete examples.