论文标题
优化完全控制的清扫过程
Optimization of Fully Controlled Sweeping Processes
论文作者
论文摘要
该论文致力于在一般的最佳控制问题中得出必要的最佳条件，用于由受控扫描过程控制的动态系统，并通过硬受控的控制动作进入多面体移动集和加性扰动。通过使用一阶和主要是二阶的变异分析和广义分化工具，我们开发了一种良好的离散近似方法，为离散时间控制系统的解决方案获得最佳条件，然后通过传递到限制的必要必要的最佳条件来确定原始控制的扫描过程的本地最小化条件，这些条件完全按照其给定的数据表示。通过解决三个非平凡的例子来说明了所获得的全面动态最佳最佳条件的效率。
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets and additive perturbations. By using the first-order and mainly second-order tools of variational analysis and generalized differentiation, we develop a well-posed method of discrete approximations, obtain optimality conditions for solutions to discrete-time control systems, and then establish by passing to the limit verifiable necessary optimality conditions for local minimizers of the original controlled sweeping process that are expressed entirely in terms of its given data. The efficiency of the obtained necessary optimality conditions for the sweeping dynamics is illustrated by solving three nontrivial examples of their own interest.
