An Optimization Approach Based Pseudospectral Method for Free‐Final‐Time Optimal Control Problems

ABSTRACT

This study extends a recently developed optimization‐based pseudospectral framework to trajectory optimization problems with unspecified terminal times, a class of optimal control problems where the unknown final time introduces significant numerical sensitivity compared to fixed‐final‐time formulations. The proposed approach proceeds by discretizing the Hamiltonian boundary value problem derived from Pontryagin's minimum principle. We then establish an error estimate for the discretization scheme and present the algorithmic enhancements needed to treat the free‐final‐time as an explicit decision variable. The performance of the method is finally demonstrated through two benchmark examples.