An Approach to Adaptive Boundary Control of Linear Stochastic Distributed Parameter Systems

Abstract

The linear distributed parameter system for the adaptive control problem is modelled by an evolution equation with an infinitesimal generator for an analytic semi group and the noise in the system is a cylindrical white noise. The unknown parameters appear affinely in both the infinitesimal generator of the semigroup and the unbounded linear transformation of the control. A family of least squares estimates of these parameters is shown to be strongly consistent. The certainty equivalence adaptive control for an ergodic quadratic cost functional is shown to be self-tuning and self-optimizing.