TOWARDS A UNIFIED THEORY OF PARAMETER ADAPTIVE-CONTROL .2. CERTAINTY EQUIVALENCE AND IMPLICIT TUNING

It is shown that for a large class of linear multivariable process models a properly designed certainty equivalence controller results in a tunable closed-loop parameterized system. The importance of this result to both the analysis and synthesis of parameter adaptive control systems is discussed. It is demonstrated by means of examples how the connection between certainty equivalence and tunability, together with the concept of tunability itself, can be used to markedly simplify the stability analysis of adaptive control systems. A new family of indirect parameterized controllers is introduced which have capabilities comparable to those of the well-known direct parameterized controllers which, for a long time, have served as basic building blocks for adaptive control systems of all types. The concept of implicit tuning is formalized and its potential importance to adaptive control is briefly discussed. It is explained how the idea of tunability can be used to analyze an implicity tuned system.