Optimal control of a perturbed sweeping process via discrete approximations
Optimal control of a perturbed sweeping process via discrete approximations
复制标题
通过离散近似对扰动扫掠过程进行优化控制
DOI：
10.3934/dcdsb.2016100
复制
发表时间：
2016
影响因子：
1.2
通讯作者：
B. Mordukhovich
中科院分区：
文献类型：
--
作者：
Tan H. Cao;B. Mordukhovich
本文讨论了一个最优控制问题的扰动扫描过程的速率无关的滞后类型所描述的控制"播放和停止”的运营商与单独控制的扰动。这个问题可以归结为动态优化的状态约束无界微分包含高度不规则的数据，不能处理的最优控制理论的微分包含的已知结果。我们开发的离散近似的方法，这使我们能够充分取代原来的最优控制问题的序列适定的有限维优化问题，其最优解强烈收敛到控制扰动扫描过程。为了解决离散化控制系统，我们得到有效的必要条件，通过使用二阶广义微分工具的变分分析，明确计算的给定问题的数据。
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled ``play-and stop" operator with separately controlled perturbations. This problem can be reduced to dynamic optimization of a state-constrained unbounded differential inclusion with highly irregular data that cannot be treated by means of known results in optimal control theory for differential inclusions. We develop the method of discrete approximations, which allows us to adequately replace the original optimal control problem by a sequence of well-posed finite-dimensional optimization problems whose optimal solutions strongly converge to that of the controlled perturbed sweeping process. To solve the discretized control systems, we derive effective necessary optimality conditions by using second-order generalized differential tools of variational analysis that explicitly calculated in terms of the given problem data.