A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 2: Application

In the first part of this paper series, a new solver, called HDDP, was presented for solving constrained, nonlinear optimal control problems. In the present paper, the algorithm is extended to include practical safeguards to enhance robustness, and four illustrative examples are used to evaluate the main algorithm and some variants. The experiments involve both academic and applied problems to show that HDDP is capable of solving a wide class of constrained, nonlinear optimization problems. First, the algorithm is verified to converge in a single iteration on a simple multi-phase quadratic problem with trivial dynamics. Successively, more complicated constrained optimal control problems are then solved demonstrating robust solutions to problems with as many as 7 states, 25 phases, 258 stages, 458 constraints, and 924 total control variables. The competitiveness of HDDP, with respect to general-purpose, state-of-the-art NLP solvers, is also demonstrated.