Robust Controller Synthesis is Convex for Systems without Control Channel Uncertainties

Chapter

Abstract

We consider an uncertain generalized plant whose control channel is not affected by uncertainties. It is shown that these configurations emerge in various concrete problems such as robust estimator or feed-forward controller design. Under the mere hypothesis that the (possibly non-linear) uncertainties are described by integral quadratic constraints, we reveal how one can translate robust controller synthesis to a problem of designing parametric and dynamic components in a standard plant configuration, and how this can be turned into a semi-definite program.

Keywords

Tral Cerone 

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References

  1. [1]
    Balakrishan, V., Vandenberghe, L.: Semidefinite programming duality and linear time-invariant systems. IEEE Trans. Aut. Contr. 48(1), 30−41 (2003)Google Scholar
  2. [2]
    Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, SIAM-MPS Series in Optimization. SIAM Publications, Philadelphia (2001)Google Scholar
  3. [3]
    Boyd, S., El Ghaoui, L., Feron, E., Balakrishan, V.: Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics 15. SIAM, Philadelphia (1994)MATHGoogle Scholar
  4. [4]
    Cerone, V., Milanese, M., Regruto, D.: Robust feedforward design for a two-degrees of freedom controller. Systems & Control Letters 56(11−12), 736-741 (2007)MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    D’Andrea, R.: Generalized l 2 synthesis, IEEE Trans. Aut. Contr. 44(6), 1145−1156 (1999)MathSciNetGoogle Scholar
  6. [6]
    D’Andrea, R.: Convex and finite-dimensional conditions for controller synthesis with dynamic integral constraints. IEEE Transactions on Automatic Control 46(2), 222−234 (2001)MathSciNetGoogle Scholar
  7. [7]
    Desoer, C., Vidyasagar, M.: Feedback Systems: Input-Output Approach. Academic Press, London (1975)Google Scholar
  8. [8]
    Dietz, S.: Analysis and control of uncertain systems by using robust semi-definite programming. Ph.D. thesis, Delft University of Technology (2008)Google Scholar
  9. [9]
    Gahinet, P., Apkarian, P.: A linear matrix inequality approach to H control. Int. J. Robust Nonlin. 4, 421−448 (1994)MathSciNetGoogle Scholar
  10. [10]
    Giousto, A., Paganini, F.: Robust synthesis of feedforward compensators. IEEE Trans. Aut. Contr. 44(8), 1578−1582 (1999)Google Scholar
  11. [11]
    Kao, C.Y., Ravuri, M., Megretski, A.: Control synthesis with dynamic integral quadratic constraints – LMI approach. In: Proc. 39th IEEE Conf. Decision and Control, pp. 1477−1482. Sydney, Australia (2000)Google Scholar
  12. [12]
    Köse, I.E., Scherer, C.W.: Robust L 2-gain feedforward control of uncertain systems using dynamic IQCs. International Journal of Robust and Nonlinear Control p. 24 (2009)Google Scholar
  13. [13]
    Masubuchi, I., Ohara, A., Suda, N.: LMI-based controller synthesis: a unified formulation and solution. Int. J. Robust Nonlin. 8, 669−686 (1998)MathSciNetGoogle Scholar
  14. [14]
    Megretski, A., Rantzer, A.: System analysis via integral quadratic constraints. IEEE T. Automat. Contr. 42, 819−830 (1997)CrossRefMathSciNetGoogle Scholar
  15. [15]
    Scherer, C.W.: Design of structured controllers with applications. In: Proc. 39th IEEE Conf. Decision and Control. Sydney, Australia (2000)Google Scholar
  16. [16]
    Scherer, C.W.: An efficient solution to multi-objective control problems with LMI objectives. Syst. Contr. Letters 40(1), 43−57 (2000)MathSciNetGoogle Scholar
  17. [17]
    Scherer, C.W.: Multi-objective control without Youla parameterization. In: S. Moheimani (ed.) Perspectives in robust control, Lecture Notes in Control and Information Sciences, vol 256, pp. 311−325. Springer-Verlag, London (2001)CrossRefGoogle Scholar
  18. [18]
    Scherer, C., Gahinet, P., Chilali, M.: Multi-objective output-feedback control via LMI optimization. IEEE T. Automat. Contr. 42, 896−911 (1997)CrossRefMathSciNetGoogle Scholar
  19. [19]
    Scherer, C.W., Köse, I.E.: Robustness with dynamic IQCs: An exact state-space characterization of nominal stability with applications to robust estimation. Automatica 44(7), 1666−1675 (2008)CrossRefGoogle Scholar
  20. [20]
    Sun, K.P., Packard, A.: Robust H 2 and H filters for uncertain LFT systems. IEEE Trans. Aut. Contr. 50(5), 715−720 (2005)MathSciNetGoogle Scholar
  21. [21]
    Veenman, J., Köroğlu, H., Scherer, C.W.: An IQC approach to robust estimation against perturbations of smoothly time-varying parameters. In: Proc. 47th IEEE Conf. Decision and Control. Cancun, Mexico (2008)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands

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