Solve the General Constrained Optimal Control Problem with Common Integration Method
Abstract
Computation of general state- and/or control-constrained Optimal Control Problems (OCPs) is difficult for various constraints, especially the intractable path constraint. For such problems, the theoretical convergence of numerical algorithms is usually not guaranteed, and the right solution may not be successfully obtained. With the recently proposed Variation Evolving Method (VEM), the evolution equations, which guarantee the convergence towards the optimal solution in theory even for the general constrained OCPs, are derived. In particular, the costate-free optimality conditions are established. Besides the analytic expressions of the costates and the Lagrange multipliers adjoining the terminal constraint, the integral equation that determines the Karush-Kuhn-Tucker (KKT) multiplier variable is also derived. Upon the work in this paper, the general constrained OCPs may be transformed to the Initial-value Problems (IVPs) to be solved, with common Ordinary Differential Equation (ODE) numerical integration methods.
Cite
@article{arxiv.1802.02140,
title = {Solve the General Constrained Optimal Control Problem with Common Integration Method},
author = {Sheng Zhang and Jin-Mei Gao},
journal= {arXiv preprint arXiv:1802.02140},
year = {2025}
}
Comments
Key words: Optimal control, path constraint, dynamics stability, variation evolution, the second evolution equation, costate-free optimality condition, Karush-Kuhn-Tucker (KKT) condition, initial-value problem. arXiv admin note: text overlap with arXiv:1801.07395, arXiv:1801.01383, arXiv:1801.10486, arXiv:1712.09702