Robust output feedback controller design: genetic algorithm approach

This paper proposes guaranteed cost design of robust output feedback controller for continuous linear parametric uncertain systems. New necessary and sufficient conditions for static output feedback stabilizability of linear continuous time systems underly the design procedure. Proposed algorithms are computationally simple and tightly connected with the Lyapunov stability theory and the LQR optimal state feedback design. The proposed approach allows for prescribing the structure of the output feedback gain matrix (including the decentralized one) by the designer. New design method proposed in this paper, exploit genetic algorithm to design robust controller with guaranteed cost for polytopic linear continuous time systems. Numerical example is given to illustrate the performance of the proposed robust controller.

[1]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[2]  Faryar Jabbari,et al.  Rbust control of linear systems with real parametric uncertainty , 1999, Autom..

[3]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[4]  Robert E. Benton,et al.  A non-iterative LMI-based algorithm for robust static-output-feedback stabilization , 1999 .

[5]  O. Toker,et al.  On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[6]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  Li Yu,et al.  An LMI approach to guaranteed cost control of linear uncertain time-delay systems , 1999, Autom..

[8]  R. Skelton,et al.  Linear quadratic suboptimal control with static output feedback , 1994 .

[9]  V. Veselý,et al.  Robust Controller Design Using Genetic Algorithms , 2000 .

[10]  H. Imai.  Robust output regulation for linear systems with structured uncertainty , 1997 .

[11]  Carlos E. de Souza,et al.  A necessary and sufficient condition for output feedback stabilizability , 1995, Autom..

[12]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[13]  Chaouki T. Abdallah,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[15]  L. El Ghaoui,et al.  Synthesis of fixed-structure controllers via numerical optimization , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[16]  Yong-Yan Cao,et al.  Static output feedback simultaneous stabilization: ILMI approach , 1998 .

[17]  Mohamed Darouach,et al.  On the robustness of linear systems with nonlinear uncertain parameters , 1998, Autom..

[18]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[19]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[20]  Michael G. Safonov,et al.  Global optimization for the Biaffine Matrix Inequality problem , 1995, J. Glob. Optim..