Abstract
The control problem of a stochastic system including distributed parameter subsystems of transportation type is discussed. The system discussed in this paper is a mixed parameter system which is described by a system of ordinary differential equations and hyperbolic partial differential equations both perturbed by Gaussian white noise. The stochastic mathematical model of the system is formulated as stochastic integral equations, and a sufficient condition, under which the model has a unique solution, is derived. The optimal control problem of the linear system for a quadratic cost performance is discussed, and a sufficient condition for the optimal control is obtained. Applying this condition, the optimal control can be realized by linear feedback of the state {x(t), ξ(t, )}, and the optimal feedback gain is obtained as the solution of the Riccati type differential equation.
