Quantitative Characterization of Easily Controllable Systems Considering Physical Constraints

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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.