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Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems

Author

Listed:
  • K. Malanowski

    (Polish Academy of Sciences)

  • H. Maurer

    (Westfälische Wilhelms-Universität)

  • S. Pickenhain

    (Westfälische Wilhelms-Universität)

Abstract

Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers. The obtained SSC involve the strict Legendre-Clebsch condition and the solvability of an auxiliary Riccati equation. They are weakened by taking into account the strongly active constraints.

Suggested Citation

  • K. Malanowski & H. Maurer & S. Pickenhain, 2004. "Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 595-617, December.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:3:d:10.1007_s10957-004-5725-0
    DOI: 10.1007/s10957-004-5725-0
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    References listed on IDEAS

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    1. Dirk Augustin & Helmut Maurer, 2001. "Computational Sensitivity Analysis for State Constrained Optimal Control Problems," Annals of Operations Research, Springer, vol. 101(1), pages 75-99, January.
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    Cited by:

    1. M. M. A. Ferreira & A. F. Ribeiro & G. V. Smirnov, 2015. "Local Minima of Quadratic Functionals and Control of Hydro-electric Power Stations," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 985-1005, June.
    2. Gerardo Sánchez Licea, 2021. "Weak Measurable Optimal Controls for the Problems of Bolza," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    3. Leonardo Mazzini, 2023. "Neighboring Optimal Guidance in Bang Bang Control with Target," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 310-336, October.
    4. M. Gerdts, 2006. "Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 443-462, September.
    5. Enes Kacapor & Teodor M. Atanackovic & Cemal Dolicanin, 2020. "Optimal Shape and First Integrals for Inverted Compressed Column," Mathematics, MDPI, vol. 8(3), pages 1-14, March.

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