NECESSARY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS BY MULTIVALUE NONLINEAR EQUATIONS
多值非线性系统最优控制的一阶必要条件

In this paper,necessary conditions for optimal control problems by multivalue nonlinearequations are considered.First,we use the smoothing method in such a way that it is ap-proximated by a family of smoothing problems for which the necessary conditions are obtai-ned for optimlity.Then,the necessary conditions are deduced for optimality of the originalcontrol problem under some assumptions.Also,these abstract results are applied to the distri-buted and boundary control problems governed by parabolic differential equations.