Interior Point Differential Dynamic Programming

This brief introduces a novel differential dynamic programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely feasible- and infeasible-IPDDP algorithms, are developed using primal–dual interior-point methodology, their local quadratic convergence properties characterized. We show that the stationary points of algorithms perturbed KKT points, thus can be moved arbitrarily close to locally solution. Being free from burden active-set methods, it handle nonlinear state input constraints without discernible increase in its computational complexity relative unconstrained case. The performance proposed is demonstrated numerical experiments on three different problems: control-limited inverted pendulum, car-parking, unicycle motion obstacle avoidance.