联合机会约束动态规划

M. Ono, Y. Kuwata, B. Balaram
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引用次数: 17

摘要

提出了一种新的联合机会约束动态规划算法,该算法明确地限定了满足给定状态约束的失效概率。现有的约束动态规划方法不能处理联合机会约束,因为它们的应用仅限于与成本函数相同形式的约束,即对一阶段成本总和的期望。我们克服了这一挑战,通过将联合机会约束重新表述为对指标函数和的期望约束,可以通过对偶优化问题将其纳入成本函数。结果表明,原始变量可通过标准动态规划优化,对偶变量可通过指数收敛的寻根算法优化。严格推导了原始和对偶目标值的误差界。我们在路径规划问题上演示了该算法,以及火星进入、下降和着陆的最优控制问题。模拟是使用火星的真实地形数据进行的,每个时间步长有400万个离散状态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Joint chance-constrained dynamic programming
This paper presents a novel joint chance-constrained dynamic programming algorithm, which explicitly bounds the probability of failure to satisfy given state constraints. Existing constrained dynamic programming approaches cannot handle a joint chance constraint since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.
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