切换非线性系统最优控制的弱拓扑
On Weak Topology for Optimal Control of Switched Nonlinear Systems
摘要：
由于切换控制输入的离散性，切换系统的最优控制具有挑战性。基于嵌入的方法解决了这一挑战，通过解决相应的放松最优控制问题，只有连续的输入，然后投影放松的解决方案，以获得原始问题的最优切换解决方案。本文提出了一种新的思想，认为嵌入为基础的方法作为一个拓扑结构的变化，在优化空间，从而在一个一般的程序来构建一个切换最优控制算法，保证收敛到一个局部优化。我们的结果提供了一个统一的拓扑结构为基础的框架，分析和设计各种嵌入式算法在解决切换最优控制问题，并包括许多现有的方法作为特例。
英文摘要：
Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only continuous inputs, and then projecting the relaxed solution back to obtain the optimal switching solution of the original problem. This paper presents a novel idea that views the embedding-based approach as a change of topology over the optimization space, resulting in a general procedure to construct a switched optimal control algorithm with guaranteed convergence to a local optimizer. Our result provides a unified topology based framework for the analysis and design of various embedding-based algorithms in solving the switched optimal control problem and includes many existing methods as special cases.
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