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Extended-Space Control Design with Parameter-Dependent Lyapunov Functions

具有参数相关李亚普诺夫函数的扩展空间控制设计

基本信息

批准号：
14550445
负责人：
SHIMOMURA Takashi
金额：
$ 1.6万
依托单位：
Osaka Prefecture University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

This research attempts to establish a new framework of control design that allows for parameter-dependent Lyapunov functions. In this research, we particularly consider multiobjective control, robust control for polytopic uncertainties, and gain-scheduled control for LPV (Linear Parameter-Varying) systems. Through inverse use of the elimination lemma, we translate a given BMI(Bilinear Matrix Inequality) problem into an extended LMI(Linear Matrix Inequality) problem while introducing a virtual parameter. In this translation, the original BMI variables are split into two different LMI terms at the expense of generating some new BMI terms with the virtual parameter, and we can solve the problem with distinct Lyapunov solutions. In other words, we can solve mixed problems or matrix polytope problems with parameter-dependent Lyapunov functions. Based on this idea, we develop a theory described in detail and verify the applicability of the proposed method through some numerical design exampl … More es. In 2002, we have formulated extended LMI representations of Lyapunov stability, H2 control, and H∞ control. Combining them, we have successfully solved multiobjective control design problems with distinct Lyapunov solutions. In 2003, we have formulated extended LMI formulations of both robust control for polytopic uncertainties and gain-scheduled control for LPV systems. In every case, the past conservatism of common Lyapunov solutions has been considerably improved. In robust H2 control in matrix polytope problems, we cannot know which vertex achieves the worst H2 cost in advance. In 2004, we have derived an excellent formulation in which the worst H2 cost is minimized even though we cannot which one achieves it in advance. Moreover, a condition regarding dP/dt should be included in the formulation for gain-scheduled control, where the Lyapunov function is given by Ψ=x'Px. In 2004, we have successfully included a condition of dP/dt and reduced it to a set of conditions at vertices. Less

这项研究试图建立一种新的控制设计框架，允许参数依赖的Lyapunov函数。在这项研究中，我们特别考虑了多目标控制、多面体不确定性的鲁棒控制以及线性变参数系统的增益调度控制。通过利用消元引理，我们将一个给定的BMI(双线性矩阵不等式)问题转化为一个扩展的LMI(线性矩阵不等式)问题，同时引入一个虚拟参数。在这个转换中，原始的BMI变量被分成两个不同的LMI项，代价是用虚拟参数产生一些新的BMI项，我们可以用不同的Lyapunov解来解决这个问题。换言之，我们可以用参数依赖的Lyapunov函数来解决混合问题或矩阵多胞问题。基于这一思想，我们建立了详细的理论描述，并通过…的数值设计实例验证了该方法的适用性更多的ES。2002年，我们建立了Lyapunov稳定性、H_2控制和H_∞控制的扩展线性矩阵不等式表示。结合它们，我们成功地解决了具有不同Lyapunov解的多目标控制设计问题。2003年，我们建立了多面体不确定性的鲁棒控制和LPV系统的增益调度控制的扩展LMI公式。在每种情况下，通常的李亚普诺夫解过去的保守性都有了很大的改善。在矩阵多面体问题的鲁棒H2控制中，我们不能预先知道哪个顶点达到最差的H2代价。2004年，我们推导出了一个极好的公式，其中最坏的H2成本最小化，即使我们不能提前实现它。此外，关于dp/dt的条件应该包含在增益调度控制的公式中，其中李亚普诺夫函数由Ψ=x‘Px给出。2004年，我们成功地包含了dp/dt的一个条件，并将其化为一组顶点条件。较少