Trajectory Parameterization and Evolutionary Search for Constrained Optimal Control

In direct methods for constrained optimal control, accuracy depends on two things at once: the approximation space and the search applied to it. In this paper, we investigate that dependence by separating the two. A hybrid polynomial–Fourier trial space is searched by a real-coded genetic algorithm with local refinement, by a covariance-adapting evolution strategy, and by multistart of a local method, and each result is measured against the best solution the trial space itself contains. The expansion satisfies the initial conditions identically and the dynamics by construction rather than at collocation points; the control follows by inverting the dynamics, and constraints enter as blocks of algebraic rows. Nine benchmarks are solved on seven trial bases under one verification protocol, with every reference value computed here and verified independently. For the six convex problems, the best attainable value is computable, and the assisted scheme reaches it on every tested basis to a gap of at most 10−6; on the three nonconvex problems, it returns audit-admissible solutions above the feasibility threshold, under one fixed setting whose variation leaves the reported accuracy unchanged over the ranges examined. Two practical conditions are established: the trial family is over-complete and must be orthonormalized before any population-based search, and feasibility must be audited, not assumed. The accuracy attained proves not to be specific to the search: the evolution strategy reaches the same limit without local refinement, and multistart attains it on the nonconvex problems; so, what is measured is the trial space rather than the solver.