CDS Lecture Series 1999

Monday, May 24, 1999, 2:00 p.m.

A. Steven Morse
Center for Computational Vision and Control
Department of Electrical Engineering
Yale University

Scale Independent Hysteresis Switching and Some of Its Applications

``Scale-independence'' is a property of certain switching algorithms used in an adaptive context which is key to proving an algorithm's correctness when operating in the face of noise and disturbance inputs. The concept of dwell-time switching, exploited in our earlier work on supervisory control, has the advantage of being scale-independent. Unfortunately, the existence of a prescribed dwell-time makes it impossible to rule out the possibility of finite escape in applications of dwell-time switching to the adaptive control on nonlinear systems. On the other hand, the popular idea of hysteresis switching, originally devised by Middleton, Goodwin, Hill and Mayne, does not have the shortcoming. Unfortunately, hysteresis switching is not a scale-independent algorithm. Moreover, to date it is not known how to analyze systems employing hysteresis switching except in higly unrealistic [noise free, exact matching] situations when switching necessarily in finite time. In this talk we describe, analyse, and compare with dwell-time and hysteresis switching, a new form of chatter-free switching which does not employ a prescribed dwell-time and which is scale independent. To demonstrate the switching logic's utility, we consider its use as a component of an estimator-based supervisor whose purpose is to orchestrate the switching of a sequence of candidate set-point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a siso linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the set-point tracking problems, were the process's transfer function to be one of the members of the subclass. It is shown that if the number of candidate controllers is finite, it is possible to derive in a straight forward manner a reasonably explicit formula for the exponentially weighted L2 gain induced between the supervisory control system's disturbance input and its output tracking error.

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