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
DOI: 10.12677/AAM.2016.54089, PDF,    科研立项经费支持
作者: 杨小杭, 张莹：浙江师范大学数理与信息工程学院，浙江 金华；徐应涛：浙江师范大学行知学院，浙江 金华；杜林岳：浙江师范大学人事处，浙江 金华
关键词: 压缩不动点定理；控制参数化方法；最优性条件；Contraction Fixed Point Theorem； Control Parameterization Method； Optimality Condition
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.
文章引用：杨小杭, 徐应涛, 张莹, 杜林岳. 一类离散时间最优控制问题的一阶最优性条件[J]. 应用数学进展, 2016, 5(4): 773-782. https://dx.doi.org/10.12677/AAM.2016.54089

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