Abstract
In this paper, we discuss the problem of the optimal control for a quadratic performance index of a generalized linear system with time-delay. The optimal problem is formulated for a coupled system composed of a lumped parameter subsystem and a distributed parameter subsystem corresponding to a group of time-delay elements. This system includes not only an ordinary system with pure time delay, but also a wide class of distributed parameter systems which are described by first order partial differential equations. Optimal control is derived by applying the principle of optimality, and is given in the form of a linear combination of the states of both subsystems. The optimal feedback gains satisfy the system of Riccati type partial and ordinary differential equations.
The numerical method for solving the obtained Riccati type differential equations is discussed. The partial differential operator is replaced by the difference operator to obtain a set of ordinary differential equations, which are integrated numerically by the Runge-Kutta method. From computational experience, it is expected that the dependence of the accuracy on the grid size is less than that of a conventional difference-difference equation method.
