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Synthesis of Optimal Robust H ∞-Control by Convex Optimization Methods

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Abstract

It is shown that the synthesis of robust H ∞-control with respect to the output for systems with unknown limited parameters reduces to the solution of an optimization problem under constraints prescribed by a system of linear matrix inequalities. For this kind of problems, an optimization algorithm implemented with the use of standard procedures of the MATLAB package is suggested.The algorithm effectiveness is illustrated by the example of an optimal dampening of vibrations of a parametrically perturbed pendulum.

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REFERENCES

  1. Doyle, J.C., Glover, K., Khargonekar, P.P., et al., State-Space Solutions to Standard H2-and H8-Control Problems, IEEE Trans. Automat. Control, 1989, vol. 34, no. 8, pp. 831–847.

    Google Scholar 

  2. Iwasaki, T. and Skelton, R.E., All Controllers for the General H8-Control Problem: LMI Existence Conditions and State Space Formulas, Automatica, 1994, vol. 30, no. 8, pp. 1307–1317.

    Article  Google Scholar 

  3. Gahinet, P. and Apkarian, P., A Linear Matrix Inequality Approach to H8-Control, Int. J. Robust Nonlinear Control, 1994, vol. 4, pp. 421–448.

    Google Scholar 

  4. Gahinet, P., Nemirovski, A., Laub, A., and Chilali, M., LMI Control Toolbox. For Use with MATLAB, Natick: The Math. Works, 1995.

  5. Savkin, A.V. and Petersen, I.R., A Connection between H8-Control and the Absolute Stability of Uncertain Systems, Syst. Control Lett., 1994, vol. 23, pp. 197–203.

    Article  Google Scholar 

  6. Kogan, M.M., Synthesis of Robust H8-Suboptimal Controllers as a Solution of the Differential Game under Uncertainty Conditions: The Direct and the Inverse Problem, Avtom. Telemekh., 2000, no. 7, pp. 109–120.

    Google Scholar 

  7. Doyle, J.C., Synthesis of Robust Controllers and Filters with Structured Plant Uncertainty, Proc. IEEE Conf. Decision Control, San Antonio, 1983.

  8. Megretski, A., Necessary and Sufficient Condition of Stability: A Muli-loop Generalization of the Circle Criterion, IEEE Trans. Automat. Control, 1993, vol. 38, pp. 753–756.

    Article  Google Scholar 

  9. Safonov, M.G., L8-Optimal Sensitivity Versus Stability Margin, Proc. IEEE Conf. Decision Control, San Antonio, 1983.

  10. Shamma, J.C., Robust Stability with Time-Varying Structured Uncertainty, IEEE Trans. Automat.Control, 1994, vol. 39, pp. 714–724.

    Article  Google Scholar 

  11. Balandin, D.V. and Kogan, M.M., Estimation of Ultimate Possibilities of Robust H8-Control of Linear Uncertain Systems, Avtom. Telemekh., 2002, no. 9, pp. 134–141.

    Google Scholar 

  12. Balandin, D.V. and Kogan, M.M., Double-Ended Estimates of a Minimum Robust H8-Norm for Uncertain Controllable Systems, Avtom. Telemekh., 2003, no. 1, pp. 105–113.

    Google Scholar 

  13. Balandin, D.V. and Kogan, M.M., On Necessary Conditions of Solvability of Multiparameter Riccati Equations in the Problem of Robust H8-Control Relative to the Output, Diff. Uravn., 2003, no. 11, pp. 1452–1456.

    Google Scholar 

  14. Balandin, D.V. and Kogan, M.M., On Calculation of a Minimum Level of Dampening of External Disturbances in the Problem of Robust H8-Control Relative to the Output, Avtom. Telemekh., 2003, no. 11, pp. 128–137.

    Google Scholar 

  15. Balandin, D.V., Ultimate Possibilities of Control of Linear Systems and Estimation of a Minimum H8-Norm, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2001, no. 6, pp. 50–56.

  16. Apkarian, P. and Gahinet, P., A Convex Characterization of Gain-Scheduled H8-Controllers, </del>IEEE Trans. Automat. Control., 1995, vol. 40, no. 5, pp. 853–864.

    Article  Google Scholar 

  17. Yamada, Y. and Hara, S., Global Optimization for H8-Control with Constant Diagonal Scaling, IEEE Trans. Automat. Control, 1998, vol. 43, no. 2, pp. 191–203.

    Article  Google Scholar 

  18. Apkarian, P. and Tuan, H.D., Robust Control via Concave Minimization Local and Global Algorithms, IEEE Trans. Automat. Control, 2000, vol. 45, no. 2, pp. 299–305.

    Article  Google Scholar 

  19. El Ghaoui, L., Balakrishnan, V., Feron, E., and Boyd, S.P., On Maximizing a Robustness Measure for Structural Nonlinear Perturbations, Proc. American Control Conf., 1992, pp. 2923–2924.

  20. Packard, A., Zhou, K., Pandey, P., Leonhardson, J., et al., Optimal Constant I/O Similarity Scaling for Full-Information and State Feedback Control Problems, Syst. Control. Lett., 1992, vol. 19, pp. 271–280.

    Article  Google Scholar 

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Authors
  1. D. V. Balandin
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  2. M. M. Kogan
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Balandin, D.V., Kogan, M.M. Synthesis of Optimal Robust H ∞-Control by Convex Optimization Methods. Automation and Remote Control 65, 1099–1109 (2004). https://doi.org/10.1023/B:AURC.0000038716.40679.9b

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  • DOI: https://doi.org/10.1023/B:AURC.0000038716.40679.9b

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