Abstract
In this paper, an approximate method of solving the optimal control problems of the system with time-delay is discussed. The mathematical model of the system with time-delay is formulated as the special case of the coupled systems of the lumped parameter subsystem and the distributed parameter subsystem. The state variables of this coupled system are infinite dimensional and some of the control variables are distributed in space. Therefore it is necessary in practice to implement the control system with a finite number of observers and a finite number of controllers. That is, one should design the practical control system for the approximated finite dimensional system. In this paper the Galerkin method is applied to obtain the approximated system. The characteristic features of this method and the results of the simulation are described.
From the computational experience, it is shown that the proposed method requires in many cases a smaller number of observers and controllers compared with the conventional finite difference method to achieve the same degree of control performance.
