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Solutions to Constrained Optimal Control Problems with Linear Systems

Author

Listed:
  • Shangrui Zhao

    (Tongji University)

  • Jiani Zhou

    (Shanghai Lixin University of Accounting and Finance)

Abstract

This paper is devoted to present solutions to constrained finite-horizon optimal control problems with linear systems, and the cost functional of the problem is in a general form. According to the Pontryagin’s maximum principle, the extremal control of such problem is a function of the costate trajectory, but an implicit function. We here develop the canonical backward differential flows method and then give the extremal control explicitly with the costate trajectory by canonical backward differential flows. Moreover, there exists an optimal control if and only if there exists a unique extremal control. We give the proof of the existence of the optimal solution for this optimal control problem with Green functions.

Suggested Citation

  • Shangrui Zhao & Jiani Zhou, 2018. "Solutions to Constrained Optimal Control Problems with Linear Systems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 349-362, August.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1308-3
    DOI: 10.1007/s10957-018-1308-3
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    References listed on IDEAS

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    1. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jinghao Zhu & Shangrui Zhao & Guohua Liu, 2014. "Solution to Global Minimization of Polynomials by Backward Differential Flow," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 828-836, June.
    3. Jinghao Zhu & Dan Wu & David Gao, 2012. "Applying the canonical dual theory in optimal control problems," Journal of Global Optimization, Springer, vol. 54(2), pages 221-233, October.
    4. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
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