Multi-objective Robust Control System Design Based on Finite Frequency KYP Lemma and Its Applications

本课题的研究目的是基于广义KYP引理（它是原KYP引理的一个有限频率版本）的分析结果，发展一种统一的控制综合理论，特别是，我们的主要重点是考虑更实际情况的系统设计方法和设计算法，综合理论的结果如下：（1）基于广义KYP引理的PID控制器综合。(2)广义KYP引理的时域解释，其中包括作为特例的频域正实性和时域无源性的等价性。这是研究非线性系统的第一步。(3)广义KYP引理的SoS（Sum of Squares）分解特征从控制的角度对被控对象的设计是有用的。(4)给出了广义KYP引理的对偶刻画及其计算复杂性分析，并基于我们的理论结果开发了一个分析/综合工具箱.我们还实现了原始-对偶算法求解广义KYP优化问题，并比较了计算成本。比较表明，由广义KYP引理导出的半正定优化问题一般都很难求解。这促使我们开发一种新的算法考虑的结构。

The purpose of this research project is to develop a unified theory of control synthesis based on the analytical results on generalized KYP lemma, which is a finite frequency version of the original KYP lemma Especially, our main focus are on a systematic design method considering the more practical situations and on the design algorithms.The results on the synthesis theory are as follows:(1) PID controller synthesis based on the generalized KYP lemma.(2) A time-domain interpretation of the generalized KYP lemma, which includes an equivalence of positive-realness in frequency-domain and passivity in time-domain as a special case. It is a first step of the investigation for nonlinear systems.(3) An SoS (Sum of Squares) decomposition characterization of the generalized KYP lemma The result is useful for plant design from the view point of control.(4) A dual characterization of the generalized KYP lemma and its computational complexity analysis.A analysis/synthesis tool box has been developed based on our theoretical results. We also implemented primal-dual algorithms for solving the generalized KYP based optimization problems and compared the computational costs. The comparison shows that the positive semi-definite optimization problems derived from the generalized KYP lemma are very hard to solve in general. This motivates us to develop a new algorithm considering the structure.