Nonlinear programming

Physics

Aerospace engineering

Nonlinear system

Inverted pendulum

Mathematics

Dynamic programming

Economic growth

Differential dynamic programming

Mathematical optimization

Engineering

Interior point method

Artificial intelligence

Economics

Control (management)

Convergence (economics)

Computer science

Karush–Kuhn–Tucker conditions

Quantum mechanics

Quadratic programming

Control theory (sociology)

Optimal control

Differential (mechanical device)

IEEE Transactions on Control Systems Technology

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 a primal–dual interior-point methodology, and their local quadratic convergence properties are characterized. 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.

Interior Point Differential Dynamic Programming