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Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations

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  • Weilong You

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Fu Zhang

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

This paper applies the Method of Successive Approximations (MSA) based on Pontryagin’s principle to solve optimal control problems with state constraints for semilinear parabolic equations. Error estimates for the first and second derivatives of the function are derived under L ∞ -bounded conditions. An augmented MSA is developed using the augmented Lagrangian method, and its convergence is proven. The effectiveness of the proposed method is demonstrated through numerical experiments.

Suggested Citation

  • Weilong You & Fu Zhang, 2025. "Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations," Mathematics, MDPI, vol. 13(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1143-:d:1624533
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    References listed on IDEAS

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    1. R. W. Beard & G. N. Saridis & J. T. Wen, 1998. "Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 589-626, March.
    2. Wei Kang & Lucas C. Wilcox, 2017. "Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations," Computational Optimization and Applications, Springer, vol. 68(2), pages 289-315, November.
    3. S. C. Beeler & H. T. Tran & H. T. Banks, 2000. "Feedback Control Methodologies for Nonlinear Systems," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 1-33, October.
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