Self-Optimality of Adaptive Control Systems Based on the Certainty Equivalence Principle

Abstract

In this paper, we consider a general adaptive control scheme based on the recursive least squares identification technique. The control is performed by applying any control law in a certainty equivalent fashion. First, a stability result is proven, which does not require the systea to be minimum-phase. Then, it is shown that on the grounds of the stability property the control system attains the asymptotic optimality. These results constitute a fundamental step forward in the comprehension of general adaptive control schemes of possibly nonminimum phase plants.