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Disturbance Attenuation In Control Systems

Author

Listed:
  • HANS W. KNOBLOCH

    (Mathematisches Institut, Universität Würzburg, Würzburg, 97074, Germany)

Abstract

The paper deals with standard mathematical models for nonlinear affine control systems with two (vector-valued) inputsu(=control) andw(unknown except for a bound for the sup-norm). Interpretation of this scenario and its wide range of applications (in control and differential game theory): See the introduction. The main result of the paper is the presentation of a dissipation equality which seems to be new and which is the result of a special control strategy (discretized state feedback, see the introduction). Combination with Lyapunov techniques leads to a concrete proposal for stabilizing disturbed control system. The mathematical background — which is worked out in detail — amounts to an explicit integration of the Hamilton-Jacobi partial differential equation via the method of characteristics.

Suggested Citation

  • Hans W. Knobloch, 2005. "Disturbance Attenuation In Control Systems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 261-283.
    • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:03:n:s0219198905000521
    DOI: 10.1142/S0219198905000521
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    More about this item

    Keywords

    Stabilization; identification; adaption of nonlinear control systems; uncertain dynamics; multi-person differential games; Hamilton-Jacobi partial differential equation;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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