Optimal boundary control for a linear stochastic distributed parameter system using functional analysis

Abstract

So as to investigate the optimal control problem for a class of stochastic distributed parameter systems, we newly introduce the methods using functional analysis. We derive the Hamilton-Jacobi equation in a Hilbert space and treat the optimal boundary control problem with the quadratic cost functional for a linear distributed parameter system subject to both additive and statedependent noises. Furthermore from the viewpoint of design techniques for the optimal controller, we briefly discuss the pointwise control problem.