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Optimality and Tractability in Stochastic Nonlinear Control
arXiv - CS - Systems and Control Pub Date : 2020-04-01 , DOI: arxiv-2004.01041
Mohamed Naveed Gul Mohamed, Suman Chakravorty, Ran Wang

We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's infamous "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop deterministic problem from the current state, as in the so-called Model Predictive Control (MPC) approach, results in the true global stochastic optimal policy. This result holds irrespective of the attendant uncertainty.

中文翻译:

随机非线性控制中的最优性和可追踪性

我们考虑非线性随机最优控制问题。由于贝尔曼臭名昭著的“维度诅咒”,这个问题从根本上被认为是难以解决的。我们提出的结果表明,从当前状态重复解决开环确定性问题,如在所谓的模型预测控制 (MPC) 方法中,会产生真正的全局随机最优策略。无论伴随的不确定性如何,该结果都成立。
更新日期:2020-10-29
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