We study some nonlinear optimal control problems under state constraint. We construct extremal flows by differential-algebraic equations to solve an optimal control problem subject to mixed control-state constraint. Then we present an approximation approach to the state constraint optimal control problem.
Cite this paper
Zhu, J. (2025). On Nonlinear Optimal Control Problems under State Constraint. Open Access Library Journal, 12, e14454. doi: http://dx.doi.org/10.4236/oalib.1114454.
Martens, B. and Gerdts, M. (2020) Convergence Analysis for Approximations of Optimal Control Problems Subject to Higher Index Differential-Algebraic Equations and Mixed Control-State Constraints. SIAM Journal on Control and Opti-mization, 58, 1-33. https://doi.org/10.1137/18m1219382
Crandall, M.G. and Li-ons, P. (1983) Viscosity Solutions of Hamilton-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. (2023) 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
