Optimal Methods For Optimizing Pulse-Perturbed Systems

This problem is highly discussed in contemporary world.For the nonlinear problem,it is considered the singular perturbation method,which is one of the most effective for approximating the exact solution.This thesis aims to study the optimal control problems with small parameter,four sections are included.In Introduction part,the development of singularly perturbed optimal control problems with small parameter and some specific problems are reviewed,some basic concepts and main methods are introduced,the existing problems are listed.In chapter one,the optimal control problem with small parameter and with internal pulsestep is considered,for discussing the existence of solution to this class of problem,the sufficient condition,the necessary condition and the solvability condition of existence are proposed,the asymptotic expression of solution is given,the remainder is estimated,and the problem is simulated.In chapter two,a class of optimal control problem with small parameter under weak control condition is discussed,based on the solvability condition of zero-order approximation,the necessary condition for existence of solution to this class of problem is given through the adaptive method,consistently effective asymptotic expansion is constructed,and the problem is simulated.In chapter three,a class of control-limited linear singularly perturbed optimal control problem is studied,the existence of solution is discussed by using asymptotic expansion method,the asymptotic expression of solution is given,finally,the algorithm is used to simulate the problem of controlling the oscillations of a mathematical pendulum.Thus,in general,this thesis is devoted to a constructive approach to the problem of asymptotic solution of perturbed optimal control problems of Mayer type.