  This paper 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, and their local quadratic convergence properties are
characterised. We show that the stationary points of the algorithms are the
perturbed KKT points, and thus can be moved arbitrarily close to a locally
optimal solution. Being free from the burden of the active-set methods, it can
handle nonlinear state and input inequality constraints without a discernible
increase in its computational complexity relative to the unconstrained case.
The performance of the proposed algorithms is demonstrated using numerical
experiments on three different problems: control-limited inverted pendulum,
car-parking, and unicycle motion control and obstacle avoidance.

Systems and Control;Systems and Control;Optimization and Control