Design of mixed H-two/H-infinity optimal control systems using multiobjective differential evolution algorithm

In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective optimization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.

[1]  Ujjwal Maulik,et al.  Modified differential evolution based fuzzy clustering for pixel classification in remote sensing imagery , 2009, Pattern Recognit..

[2]  R.H.C. Takahashi,et al.  H/sub 2//H/sub /spl infin// filter design for systems with polytope-bounded uncertainty , 2006, IEEE Transactions on Signal Processing.

[3]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

[4]  Ricardo H. C. Takahashi,et al.  H/sub 2/ and H/spl infin/ e-guaranteed cost computation of uncertain linear systems , 2007 .

[5]  Ricardo H. C. Takahashi,et al.  H 2 /H infinity filter design for systems with polytope-bounded uncertainty. , 2006 .

[6]  Ricardo H. C. Takahashi,et al.  H2/H∞ filter design for systems with polytope-bounded uncertainty , 2006 .

[7]  Chein-Chung Sun,et al.  H2∕H∞ Robust Static Output Feedback Control Design via Mixed Genetic Algorithm and Linear Matrix Inequalities , 2005 .

[8]  H. X. Araujo,et al.  Robust output feedback controller design via genetic algorithms and LMIs: the mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// problem , 2004, Proceedings of the 2004 American Control Conference.

[9]  Hung-Yuan Chung,et al.  GA-based H2/H∞ static output feedback design with average performance concept and techniques of family of polynomials , 2009, Expert Syst. Appl..

[10]  The Multiobjective H2/H8/Impulse-to-peak Output-Feedback Control via LMI Optimization , 2009, 2009 International Conference on Advanced Computer Control.

[11]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[12]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[13]  K. Price.  Differential evolution vs. the functions of the 2/sup nd/ ICEO , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[14]  Ricardo H. C. Takahashi,et al.  Estimation of Pareto sets in the mixed control problem , 2004, Int. J. Syst. Sci..

[15]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[16]  Lianghong Wu,et al.  Self-adapting control parameters modified differential evolution for trajectory planning of manipulators , 2007 .

[17]  R. Takahashi,et al.  Improved optimisation approach to the robust H2/H∞ control problem for linear systems , 2005 .

[18]  Shinn-Ying Ho,et al.  OSA: orthogonal simulated annealing algorithm and its application to designing mixed H2/H∞ optimal controllers , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[19]  Peng Shi,et al.  Robust Hinfinity output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: An LMI approach , 2006, Inf. Sci..

[20]  Ian Griffin,et al.  Linear matrix inequalities and evolutionary optimization in multiobjective control , 2006, Int. J. Syst. Sci..

[21]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[22]  Zhun Fan,et al.  Improved Differential Evolution Based on Stochastic Ranking for Robust Layout Synthesis of MEMS Components , 2009, IEEE Transactions on Industrial Electronics.

[23]  L. Coelho,et al.  Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect , 2006, IEEE Transactions on Power Systems.

[24]  Frederico G. Guimarães,et al.  Design of mixed H2/Hinfinity control systems using algorithms inspired by the immune system , 2007, Inf. Sci..

[25]  Nong Zhang,et al.  Multiobjective Static Output Feedback Control Design for Vehicle Suspensions , 2008 .

[26]  M. Farhoodi,et al.  A case study of the multiobjective H2/H∞ control via finite dimensional Youla parameterization and LMI optimization , 2007, IECON 2007 - 33rd Annual Conference of the IEEE Industrial Electronics Society.

[27]  Chih-Lyang Hwang,et al.  Mixed H2/Hspl infin/ design for a decentralized discrete variable structure control with application to mobile robots , 2005, IEEE Trans. Syst. Man Cybern. Part B.