Journal
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
Volume 29, Issue 6, Pages 2720-2727Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCST.2021.3049416
Keywords
Heuristic algorithms; Convergence; Optimal control; Optimization; Dynamic programming; Prediction algorithms; Trajectory; Differential dynamic programming (DDP); finite horizon optimal control; interior point methods; numerical methods
Funding
- Australian Government [AUSMURIB000001]
- ONR MURI [N00014-19-1-2571]
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This brief introduces a novel differential dynamic programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, feasible- and infeasible-IPDDP algorithms, are developed using a primal-dual interior-point methodology, and their local quadratic convergence properties are characterized. The performance of the proposed algorithms is demonstrated using numerical experiments on three different problems, showing that they can handle nonlinear constraints without a discernible increase in computational complexity.
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.
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