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Passivity-based optimal control of discrete-time nonlinear systems

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Języki publikacji
EN
Abstrakty
EN
In this paper, a passivity-based optimal controlmethod for a broad class of nonlinear discrete-time systems is proposed. The resulting control law is a static output feedback law which is practically preferred with respect to the state feedback law and is simple to implement. The control law has a general structure with adjustable parameters which are tuned, using an optimization method (genetic algorithm), to minimize an arbitrary cost function. By choosing this cost function it is possible to shape the transient response of the closed-loop system, as it is desirable. An illustrative ex ample shows the effectiveness of the proposed approach.
Rocznik
Strony
627--637
Opis fizyczny
Bibliogr. 23 poz., wykr.
Twórcy
autor
  • School of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Blvd., Shiraz, P.O. Box 71555/313, Iran
  • School of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Blvd., Shiraz, P.O. Box 71555/313, Iran
Bibliografia
  • 1. Belegundu, A.D. and Chandrupatla, T.R. (1999) Optimization Concepts and Applications in Engineering. Prentice Hall, Upper Saddle River, NJ.
  • 2. Byrnes, C.I., Isidori, A. and Willems, J.C. (1991) Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Trans. on Automatic Control, 36, 1228–1240.
  • 3. Byrnes, C.I. and Isidori, A. (1991) Asymptotic stabilization of minimum phase nonlinear systems. IEEE Trans. on Automatic Control, 35, 1122–1137.
  • 4. Byrnes, C.I. and Lin, W. (1993) Discrete-time lossless systems, feedback equivalence, and passivity. Proc. 32nd Conf. on Decision and Control. IEEE, 1775–1781.
  • 5. Byrnes, C.I. and Lin, W. (1994) Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems. IEEE Trans. on Automatic Control, 39, 83–98.
  • 6. Goldberg, D.E (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley.
  • 7. Hill, D. and Moylan, P. (1976) The stability of nonlinear dissipative systems. IEEE Trans. on Automatic Control, 21, 708–711.
  • 8. Hitz, L. and Anderson, B.D.O. (1969) Discrete positive-real functions and their application to system stability. Proceedings of IEE, 116, 153–155.
  • 9. Lewis, F.L., Vrabie, D. and Syrmos, V.L. (2012) Optimal Control, 3rd edition. Wiley.
  • 10. Lin, W. and Byrnes, C.I. (1995) Passivity and absolute stabilization of a class of discrete-time nonlinear systems. Automatica, 31, 263–267.
  • 11. Monaco, S. and Normand-Cyrot, D. (1997) On the conditions of passivity and losslessness in discrete time. Proc. of the European Control Conference, Brussels, Belgium.
  • 12. Monaco, S. and Normand-Cyrot, D. (1999) Nonlinear representations and passivity conditions in discrete time, robustness in identification and control. Lecture Notes in Control and Information Sciences, 245, 422–433.
  • 13. Navarro-Lopez, E.M. (2002) Dissipativity and passivity-related properties in nonlinear discrete-time systems. PhD thesis, Universitat Politecnica de Catalunya, Barcelona, ISBN: 84-688-1941-7.
  • 14. Navarro-Lopez, E.M., Sira-Ramirez, H. and Fossas-Colet, E. (2002) Dissipativity and feedback dissipativity properties of general nonlinear discrete-time systems. European Journal of Control, 8, 256–274.
  • 15. Navarro-Lopez, E.M. and Fossas-Colet, E. (2004) Feedback passivity of nonlinear discrete-time systems with direct input-output link. Automatica, 40(8), 1423–1428.
  • 16. Navarro-Lopez, E.M. (2005) Several dissipativity and passivity implications in the linear discrete-time setting. Mathematical Problems in Engineering, 11(6), 599–616.
  • 17. Navarro-Lopez, E.M. (2007) Qss-dissipativity and feedback QS-passivity of nonlinear discrete-time systems. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 14, 47–63.
  • 18. Navarro-Lopez, E.M. (2007) Local feedback passivation of nonlinear discretetime systems through the speed-gradient algorithm. Automatica, 43, 1302–1306.
  • 19. Nocedal, J. and Wright, S.J. (1999) Numerical Optimization. Springer.
  • 20. Sengor, N.S. (1995) Energy related concepts in nonlinear systems. PhD thesis, Istanbul Technical University, Turkey.
  • 21. Shuping, W., Guoshan, Z. and Wanquan, L. (2010) Dissipative analysis and control for discrete-time state-space symmetric systems. Proc. Control Conference (CCC). IEEE, 2010–2015.
  • 22. Willems, C. (1972) Dissipative dynamical systems. Part I: general theory. Arch. Rational Mech. Analys., 45, 325–35.
  • 23. Willems, C. (1972) Dissipative dynamical systems. Part II: linear systems with quadratic supply rates. Arch. Rational Mech. Analys., 45, 352–393.
Typ dokumentu
Bibliografia
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