On the block pulse operator method to solving nonlinear control system with time delay

The author develops a general approximation framework for use in optimal problems governed by nonlinear differential equations with time delay by means of the block pulse operator (BPO). In the framework, the problem of minimization of a cost over space is approximated by a sequence of problems requiring minimization over the image space of the BPO. In the approximating space, the method of solving for the problems can be considerably simplified and a block pulse series solution (BPSS) can be obtained. The convergence of the BPSS to the optimal control problem is proved, and the first-order convergence rate is established. Two examples are presented to illustrate the utility of this method