A Disturbance Attenuation Approach to Adaptive Control

Abstract

This paper discusses the the control of systems with poorly known, not necessarily constant parameters under the effect of process and measurement noise. To limit the effects of the uncertainties and disturbances, a disturbance attenuation function is constructed, and converted to a performance index. A multi-player game is then considered, in which the control attempts to minimize the performance index, which the uncertainties and disturbances attempt to maximize. By taking a dynamic programming approach, the problem is decomposed into a forward-looking optimal control problem and a past-time filtering problem. These are each much simpler than the original problem, allowing a larger class of problems to be tackled. Most of the results presented here are for linear systems, with some suggestions for their extension to non-linear cases.