Adaptive Boundary Control for Stochastic Heat Diffusion Equation with Unknown Potential Coefficient

Abstract

An adaptive boundary control problem for a stochastic heat diffusion equation is studied. The considered system contains the unkown potential coefficient which is a function of a spatial variable. The estimation algorithm for the unknown potential coefficient is proposed by using the stochastic approximation technique. After showing the strong consistency of the estimated parameter, the cost for the adaptive control scheme presented here is shown to converge to the optimal ergodic cost. Finally some numerical examples are shown.