Quantitative Characterization of Easily Controllable Systems Considering Physical Constraints

本研究计画的目的是探讨在物理限制下的易控制动态系统，并提出一种新的反馈控制系统中被控对象与控制器的整合设计方法。1）控制性能限制：研究了LTI系统在物理约束下的最佳H_2控制性能，包括连续系统、离散系统和采样系统。一个统一的方法来获得解析封闭形式的表达式的限制已被提出。结果清楚地表明了由被控对象增益特性以及不稳定的极点/零点所引起的恶化，并提供了一些工程应用。2）有限频率KYP引理：首先给出了S-过程是无损耗的充要条件，并利用该结果在有限频率范围和系统类别两个方面推广了Kalman-Yakubovic-Popov（KYP）引理，用一个定理统一了现有的各种版本。它已被证明，我们的结果使我们能够解决某一类系统的设计问题，在几个频率范围内的增益/相位特性的多个规格。3）非线性控制系统：研究了一类非完整系统控制的难易程度。特别地，我们证明了对于线性和非线性动力系统，都不存在连续的控制输入，使其实现对非平衡点的设定点的完全跟踪。

The purpose of the research project is to characterize easily controllable dynamical systems under physical constraints and to propose a new integrated design method for plant and controller in feedback control systems. The following three issues have been investigated.1)Control performance limitation :We have examined the best achievable H_2 control performance under physical constraints for LTI systems including continuous-time systems, discrete-time systems, and sampled-data systems. A unified approach to derive analytical closed form expressions for the limitations has been proposed. The results clearly demonstrate the deteriorations caused by the plant gain characteristics as well as unstable poles/zeros of the plant, and some engineering applications have been provided.2)Finite frequency KYP lemma :We have first developed a necessary and sufficient condition for an S-procedure to be lossless, and used the result to generalize the Kalman-Yakubovic-Popov (KYP) lemma in two aspects ---the finite frequency range and the class of systems ---and to unify various existing versions by a single theorem. It has been shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. A soft wear tool for the analysis and synthesis has been also developed on MATLAB.3)Nonlinear control system :We have investigated the easiness and difficulties of controlling a class of non-holonomic systems. Especially, we have shown that the there exists no continuous control input which achieves complete tracking with set point of non-equilibrium point for both linear and nonlinear dynamical systems.