Abstract
The optimal control problem of stochastic linear systems with time-delay is discussed. The problem is formulated as that of a coupled system of a lumped parameter sub-system and a distributed parameter sub-system which corresponds to a group of time-delay elements. This formulation clarifies that this problem can be treated as the Markovian control problem. In the framework of a class of stochastic Markovian control problem, a sufficient condition for the optimal control is obtained. Applying this condition, the optimal control for a quadratic criterion is derived.
The optimal control law can be realized by the cascade of a coupled type state estimator and a linear feedback. In other words, the optimal control is given in a form of a linear combination of state estimates x(t), ξ(t, ·) of both sub-systems. The optimal feedback gains are the solution of the Riccati type ordinary and partial differential equations, and coincide with that of the deterministic case.
