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Minimax control for nonstationary linear operator systems

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Abstract

A solution to the minimax linear-quadratic problem of control of an operator system on a semi-infinite time interval is presented. The solution is based on the abstract maximum principle, Willems’ behavioral approach, the direct method of basic operators, and a small gain theorem.

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References

  1. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-Space Solutions to Standard H 2 and H ∞ Control Problems,” IEEE Trans. Autom. Control 34(8), 831–847 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  2. B. A. Francis, A Course in H ∞ Control Theory (Springer, New York, 1987), Lect. Notes Control Inf. Sci. 88.

    MATH  Google Scholar 

  3. A. E. Barabanov and A. M. Ghulchak, “Numerical Solution and Operator Approach to H ∞ Control of Linear Delayed Systems,” in The 39th IEEE Conf. on Decision and Control, Sydney (Australia), Dec. 13–15, 2000.

  4. G. B. Afanassieva, A. E. Barabanov, and T. I. Shtanenko, “H ∞ Filtering of Linear Delayed Systems,” in Eur. Control Conf., Porto (Portugal), Sept. 4–7, 2001, Sect. Th-E08.

  5. A. E. Barabanov, “Invariance and Polynomial Design of Strategies in the Linear-Quadratic Game,” Avtom. Telemekh., No. 10, 20–46 (2006) [Autom. Remote Control 67, 1547–1572 (2006)].

  6. H. Kwakernaak, “The Polynomial Approach to H ∞-Optimal Regulation,” in H ∞-Control Theory, Ed. by C. Foias, B. Francis, J. W. Helton, H. Kwakernaak, and J. B. Pearson (Springer, Berlin, 1990), Lect. Notes Math. 1496, pp. 141–221.

    Google Scholar 

  7. J. C. Willems, “Paradigms and Puzzles in the Theory of Dynamical Systems,” IEEE Trans. Autom. Control 36(3), 259–294 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. S. Matveev and V. A. Yakubovich, Abstract Theory of Optimal Control (St. Petersburg Univ., St. Petersburg, 1994) [in Russian].

    Google Scholar 

  9. A. E. Barabanov, “Maximin Control of Delayed Systems,” Tr. Inst. Mat., Nats. Akad. Nauk Belarusi 12(2), 26–32 (2004).

    Google Scholar 

  10. A. E. Barabanov, “Solution of the Nonstationary Maximin LQ Control Problem,” in Analytic Methods of Analysis and Differential Equations: AMADE 2003, Ed. by A. A. Kilbas and S. V. Rogosin (Cambridge Sci. Publ., Cambridge, 2006), pp. 1–14.

    Google Scholar 

  11. A. E. Barabanov and A. A. Pervozvanskii, “Optimization by Frequency-Uniform Criteria (H-Theory),” Avtom. Telemekh., No. 9, 3–32 (1992) [Autom. Remote Control 53 (9), 1301–1327 (1992)].

  12. V. N. Fomin, A. L. Fradkov, and V. A. Yakubovich, Adaptive Control of Dynamic Objects (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia

    A. E. Barabanov

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  1. A. E. Barabanov
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Correspondence to A. E. Barabanov.

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Original Russian Text © A.E. Barabanov, 2008, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 262, pp. 32–49.

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Barabanov, A.E. Minimax control for nonstationary linear operator systems. Proc. Steklov Inst. Math. 262, 26–43 (2008). https://doi.org/10.1134/S0081543808030048

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