隐式时间变化演化变分不等式的适定性与输出调节
Well-Posedness and Output Regulation for Implicit Time-Varying Evolution Variational Inequalities
AI总结：
本文研究了包含时间变化多值映射的演化变分不等式类，探讨了解的存在性和唯一性条件，并基于内部模型原理设计了输出调节的反馈控制律，应用于保持多面体状态约束的系统输出调节和电力转换器控制。
摘要：
本文提出了一类包含常微分方程（ODEs）与时间变化变分不等式（VIs）的演化变分不等式（EVIs）。我们首先研究了解的存在性和唯一性条件。证明的核心思想是将系统动力学重写为微分包含，可以分解为单值Lipschitz映射和时间依赖的最大单调算子。对多值映射的正则性假设决定了所得到解的正则性。互补系统的时间依赖性作为特殊情况被研究。然后我们利用这一结果来研究由EVIs描述的系统设计状态反馈控制律以实现输出调节的问题。控制律的推导基于内部模型原理，处理了两种情况：第一种情况是当可获得完整状态反馈时推导出静态反馈控制律；第二种情况是仅假设需要调节的误差可用作测量，设计动态补偿器。应用方面，我们展示了由变分不等式解得到的控制输入如何调节系统输出并保持多面体状态约束。另一个应用是设计用于电力转换器调节的控制输入。
英文摘要：
A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first study the conditions for existence and uniqueness of solutions. The central idea behind the proof is to rewrite the system dynamics as a differential inclusion which can be decomposed into a single-valued Lipschitz map, and a time-dependent maximal monotone operator. Regularity assumptions on the set-valued mapping determine the regularity of the resulting solutions. Complementarity systems with time-dependence are studied as a particular case. We then use this result to study the problem of designing state feedback control laws for output regulation in systems described by EVIs. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available, In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed. As applications, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. Another application is seen in designing control inputs for regulation in power converters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
