Optimal Control for a Class of Parabolic System with Random Parameters
Yoshifumi SUNAHARA, ShinIchi Aihara, Fumio Kojima · Transactions of the Society of Instrument and Control Engineers · 1982
The purpose of this paper is to study the optimal control problem for a stochastic distributed parameter system with white Gaussian noise processes as coefficients in dynamics and boundary conditions of the system. By introducing the stochastic integral on a Hilbert space, the mathematical model of the system is first described by a stochastic evolution equation. Secondly, the optimal control signal under the quadratic performance criteria is derived with the aid of stochastic maximum principle. Finally, the existence property of a solution to the operator Riccati equation which plays an important role in the optimal control problem is investigated.