Bridging Direct and Indirect Methods: The Development and Benchmarking of a PMP&SQP Algorithm for Optimal Control

Optimal control problems (OCPs) are crucial in various scientific and engineering domains, necessitating efficient and robust numerical methods for their resolution. This paper introduces a numerical method, denoted as PMP&SQP, which combines the Pontryagin Minimum Principle (PMP) and Sequential Quadratic Programming (SQP). The method innovatively employs PMP for dimensionality reduction by incorporating covalent states and optimizes their initial values according to the OCP's cost function, rather than directly solving the PMP conditions. This approach takes advantage of PMP's capacity for dimensionality reduction and SQP's optimization strengths, thereby substantially enhancing computational efficiency and reducing sensitivity to initial guess variability. Benchmarking against traditional methods demonstrates the superior performance of PMP&SQP in solving large-scale OCPs and its robustness across different initial conditions.