Method Of Calculation Of The Optimal Control Parameters Of The Pulse System

Between the end of 1950s and the beginning of 1960s, Pontryagin first developed the necessary conditions of solving optimal control problems, besides Bellman derived Hmiton-Jacobi-Bellman equation with dynamic programming. But in practical, it is very difficult to get the analytical solution when we try to solve the optimal control problems, due to that the resolving is greatly affected by the control systems of differential (partial differential) equation. Therefore we pay more attention to the numerical solution of optimal control.In this paper, we consider solution of optimal control with impulsive system through optimal parameter selection problems. According to the character of impulsive system, we find a way to resolve optimal control with impulsive system after sum up the unified approach to optimal control with parameter selection problems.At first, we obtain the calculation formula of object functional grads for optimal parameterselection problems with impulsive system by variation in [0,T], then resolve the problems withmathematical programming. Second, we take , and transform theproblems into a series of approximation of the optimal parameters, according to the algorithmwhich we get from the optimal parameter selection problems, then we develop a calculationapproach to optimal control with impulsive systems and its detail process. Finally, we show thatthe numerical calculation method which we constructed is suitable by proving two convergencetheorems.