论文标题
具有控制的移动集和扰动的优化和离散近似
Optimization and Discrete Approximation of Sweeping Processes with Controlled Moving Sets and Perturbations
论文作者
论文摘要
本文讨论了一类新的最佳控制问题，用于通过可测量的控制在多面体移动集中的动力学和平滑控制方面进行可测量的控件。我们开发了一个建设性的离散近似程序，使我们能够通过可行的离散轨迹强烈近似受控扫描过程的任何可行轨迹，并且还建立了$ W^{1,2} $ - 最佳轨迹的强烈收敛，以使离散控制问题的特定控制问题与给定的持续持续范围范围的范围范围范围范围范围的局部范围范围的局部范围范围，以bolza类型的局部最小化。采用高级工具的一阶和二阶变分析分析和广义分化的工具，我们在完全根据给定数据方面完全提出的相当一般的假设，为离散的最佳解决方案提供了必要的最佳条件。获得的结果为我们提供了有效的次优（“几乎最佳”）条件，用于原始扫描控制问题，这是通过非平凡的数值示例所说明的。
This paper addresses a new class of optimal control problems for perturbed sweeping processes with measurable controls in additive perturbations of the dynamics and smooth controls in polyhedral moving sets. We develop a constructive discrete approximation procedure that allows us to strongly approximate any feasible trajectory of the controlled sweeping process by feasible discrete trajectories and also establish a $W^{1,2}$-strong convergence of optimal trajectories for discretized control problems to a given local minimizer of the original continuous-time sweeping control problem of the Bolza type. Employing advanced tools of first-order and second-order variational analysis and generalized differentiation, we derive necessary optimality conditions for discrete optimal solutions under fairly general assumptions formulated entirely in terms of the given data. The obtained results give us efficient suboptimality ("almost optimality") conditions for the original sweeping control problem that are illustrated by a nontrivial numerical example.
