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A Frequency Condition for the Generalized Recurrent Difference in the Synthesis of H∞-Suboptimal, Decentralized, and Robust Regulators

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Abstract

A new approach to designing control laws under uncertainty produces easily verifiable tests for their generalized recurrent differences and does not require the solution of matrix equations or inequalities. This test is expressed as a frequency inequality, which is verified by verifying whether a polynomial has a real positive root of odd multiplicity. The underlying principles of the method are the necessary and sufficient conditions for a given stabilizing linear feedback to be the local minimax control satisfying the Bellman–Isaac inequality in a differential game with a general quadratic functional. The design of controls for Lur'e systems and systems with uncertain bounded parameters as well as the design of H ∞-suboptimal regulators and decentralized controls for multiconnected systems with unknown cross-coupling are shown to involve a local minimax control problem.

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REFERENCES

  1. Xie, L. and de Souza, C.E., Robust H ∞ Control for Linear Systems with Norm-bounded Time-varying Uncertainty, IEEE Trans. Autom. Control, 1992, vol. 37, pp. 1188-1191.

    Google Scholar 

  2. Petersen, I.R. and McFarlane, D.C., Optimal Guaranteed Cost Control and Filtering for Uncertain Linear Systems, IEEE Trans. Autom. Control, 1994, vol. 39, pp. 1971-1977.

    Google Scholar 

  3. Colaneri, P., Geromel, J.C., and Locatelli, A., Control Theory and Design. An RH 2 and RH ∞ Viewpoint, New York: Academic, 1997.

    Google Scholar 

  4. Brusin, V.A., Frequency Criteria for the General Absolute Stabilizability Problem, Avtom. Telemekh., 2000, no. 1, pp. 11-21.

  5. Kogan, M.M., A Game Theoretic Approach to Robust Regulator Design, Avtom. Telemekh., 1998, no. 5, pp. 142-151.

  6. Kogan, M.M., Solution to the Inverse Problems of Minimax Control and Worst Case Disturbance for Linear Continuous-Time Systems, IEEE Trans. Autom. Control, 1998, vol. 43, no. 5, pp. 670-674.

    Google Scholar 

  7. Kogan, M.M., A Minimax Approach to the Design of Absolutely Stabilizing Regulators for Nonlinear Lur'e Systems, Avtom. Telemekh., 1999, no. 5, pp. 78-91.

  8. Kogan, M.M., Design of Robust H ∞-Suboptimal Regulators as a Solution of a Di_erential Game under Uncertainty: Direct and Inverse Problems, Avtom. Telemekh., 2000, no. 7, pp. 108-119.

  9. Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost' nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with a Nonunique Equilibrium State), Moscow: Nauka, 1978.

    Google Scholar 

  10. Kalman, R.E., When Is a Linear Control System Optimal?, ASME J. Basic Eng., Ser. D, 1964, vol. 86, pp. 1-10.

    Google Scholar 

  11. Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A., State-Space Solution to Standard H 2 and H ∞ Control Problems,IEEE Trans. Autom. Control, 1989, vol. 34, no. 8, pp. 831-847.

    Google Scholar 

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  1. Nizhni Novgorod University of Architecture and Construction, Nizhni Novgorod, Russia

    M. M. Kogan

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  1. M. M. Kogan
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Kogan, M.M. A Frequency Condition for the Generalized Recurrent Difference in the Synthesis of H∞-Suboptimal, Decentralized, and Robust Regulators. Automation and Remote Control 62, 943–956 (2001). https://doi.org/10.1023/A:1010201804510

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