In this paper, we use partial differential equations to deal with constraint optimal control problems. We construct extremal flows by differential-algebraic equation to approximate the optimal objective value of constraint optimal control problems. We prove a convergent theorem for an approximation approach to the optimal objective value of a state-constraint optimal control problem.
Martens, B. and Gerdts, M. (2020) Convergence Analysis for Approximations of Optimal Control Problems Subject to Higher Index Differen-tial-Algebraic Equations and Mixed Control-State Constraints. SIAM Journal on Control and Optimization, 58, 1-33. https://doi.org/10.1137/18m1219382
Zhu, J. (2017) A Feedback Optimal Control by Hamilton-Jacobi-Bellman Equation. European Journal of Control, 37, 70-74. https://doi.org/10.1016/j.ejcon.2017.05.007
Zhu, J. (2021) A Computational Approach to Non-Smooth Optimization by Diffusion Equations. Journal of Computational and Applied Mathematics, 384, Article ID: 113166. https://doi.org/10.1016/j.cam.2020.113166
Crandall, M.G. and Lions, P. (1983) Viscosity Solutions of Hamil-ton-Jacobi Equations. Transactions of the American Mathematical Society, 277, 1-42. https://doi.org/10.1090/s0002-9947-1983-0690039-8
Fleming, W.H. (1969) The Cauchy Problem for a Nonlinear First Order Partial Differential Equation. Journal of Differential Equations, 5, 515-530. https://doi.org/10.1016/0022-0396(69)90091-6
Zhu, J. (2021) A Computational Approach to Optimal Control Problems Subject to Mixed Control-State Constraints. International Journal of Control, 96, 41-47. https://doi.org/10.1080/00207179.2021.1978556
