约束条件下固定边界系统最优控制必要条件的研究

Study on Necessary Conditions for Optimal Control of Fixed Boundary Systems Under Constraint Conditions

复杂系统不仅受多个元素的影响,有时还受到一些其他条件的约束。为了求出固定边界条件下受其他条件约束的系统状态方程的最优性能指标,提出了构造辅助函数的方法。首先将整形条件约束以及非整形条件约束的系统性能指标进行结构变换,从而转化为无条件约束的性能指标表达式,再利用古典变分法中拉格朗日方程定理,求出系统达到最优时的必要条件及其证明。

Complex systems are not only affected by many elements but also constrained by some other conditions.In order to find out the optimal performance index of the system state equation constrained by other conditions under fixed boundary conditions,this paper presented a method of constructing auxiliary functions.Firstly,the performance indexes of the system with and without plastic constraints were transformed into the expression of the performance indexes without conditions.Then,the necessary conditions for the system to reach the optimum and their proof were obtained by using the Lagrange equation theorem in the classical variational method.