论文标题
内点差分动态编程
Interior Point Differential Dynamic Programming
论文作者
论文摘要
本文介绍了一种新型的差异动态编程（DDP）算法，用于解决不平等约束的离散时间有限 - 摩恩最佳控制问题。使用原始双重内点方法开发了两种变体，即可行的和不可行的IPDDP算法，其局部二次收敛属性是表征的。我们表明，算法的固定点是扰动的KKT点，因此可以任意移动到局部最佳解决方案。它不受主动设定方法的负担，它可以处理非线性状态和输入不等式约束，而不会相对于无约束的情况而明显地增加其计算复杂性。使用数值实验在三个不同的问题上证明了所提出的算法的性能：对照限制的倒置摆，公开标志和独轮车运动控制和避免障碍物。
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.
