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Optimal Control of a Constrained Bilinear Dynamic System

Author

Listed:
  • Ido Halperin

    (Ariel University)

  • Grigory Agranovich

    (Ariel University)

  • Yuri Ribakov

    (Ariel University)

Abstract

In this paper, an optimal feedback, for a free vibrating semi-active controlled plant, is derived. The problem is represented as a constrained optimal control problem of a single input, free vibrating bilinear system, and a quadratic performance index. It is solved by using Krotov’s method and to this end, a novel sequence of Krotov functions that suits the addressed problem, is derived. The solution is arranged as an algorithm, which requires solving the states equation and a differential Lyapunov equation in each iteration. An outline of the proof for the algorithm convergence is provided. Emphasis is given on semi-active control design for stable free vibrating plants with a single control input. It is shown that a control force, derived by the proposed technique, obeys the physical constraint related with semi-active actuator force without the need of any arbitrary signal clipping. The control efficiency is demonstrated with a numerical example.

Suggested Citation

  • Ido Halperin & Grigory Agranovich & Yuri Ribakov, 2017. "Optimal Control of a Constrained Bilinear Dynamic System," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 803-817, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1095-2
    DOI: 10.1007/s10957-017-1095-2
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    References listed on IDEAS

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    1. Seierstad, Atle & Sydsaeter, Knut, 1977. "Sufficient Conditions in Optimal Control Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 367-391, June.
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    Cited by:

    1. Ido Halperin & Grigory Agranovich & Yuri Ribakov, 2020. "Extension of the Constrained Bilinear Quadratic Regulator to the Excited Multi-input Case," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 277-292, January.
    2. Yusheng Zhou & Zaihua Wang & Kwok-wai Chung, 2019. "Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 634-652, May.

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