一类离散时间最优控制问题的一阶最优性条件

First-Order Optimality Conditions for a Class of Discrete-Time Optimal Control Problems

摘要: 本文对一类离散时间的控制问题，提出了存在唯一解的Lipschitz条件，并进一步地，引进控制参数化方法定义控制变量转化函数，将最优控制问题等价转化为非线性可微规划问题，得到了此类最优控制问题的一阶最优性条件。最后，给出两个算例用以验证如上提出的一阶最优性条件。

Abstract: In this paper, we give the Lipschitz condition for a class of discrete-time control problems in which the system has unique solution. Further, we present the control variable transformation function by using the control parameterization method. As a result, the optimal control problem we are considering is converted to a nonlinear differentiable programming problem. Then we put forward a class of first-order optimality conditions for this optimal control problem. Finally, two examples are provided to demonstrate the effectiveness of the proposed first-order optimality conditions.