Optimal control of a class of linear stochastic distributed-parameter systems

The paper treats the optimal distributed and boundary control problem for a general class of linear stochastic distributed-parameter systems. A quadratic cost functional is used, and the stochastic distributed Hamilton-Jacobi equation, which is derived by the dynamic-programming technique, is solved explicitly. Analogously to the lumped-parameter case, the result is a pair of linear optimal feedback controllers, their common weighting function being described by a matrix partial-integrodilferential equation of the Riccati form. When the state of the system is not exactly measured, the distributed Kalman´s filter, derived in a recent paper, is used, the decoupling of the optimal controllers and the optimal estimator being proved. Kalman´s duality principle is extended to the distributed systems under investigation, the canonical equations of Hamilton are derived and a version of Pontryagin´s minimum principle is proved.