Unfalsified Control for Slowly Varying Plants Using Fading Memory and Windowing

Abstract

A new cost function with fading memory and a finite-duration time-window is introduced in order to limit the effect of old data in unfalsified adaptive control applications where the plant varies slowly or infrequently with time. The effectiveness of the approach is demonstrated via a simple simulation in which a plant with a gain, which switches periodically, is stabilized by a time-windowed unfalsified adaptive control law that switches between two candidate PID controllers, neither of which alone would be able to stabilize the time-varying plant without switching. The result demonstrates that time-windowed/fadingmemory unfalsified methods can be effective for adaptive control of varying plants, even when the plant fails to satisfy the usual ‘feasibility’ requirement of unfalsified control that it must be stabilizable by one of the candidate controllers.