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.