On the Feedback Law in Stochastic Optimal Nonlinear Control
On the Feedback Law in Stochastic Optimal Nonlinear Control
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DOI：
10.23919/acc53348.2022.9867673
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
M. Mohamed;S. Chakravorty;R. Goyal;Ran Wang
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文献类型：
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作者：
M. Mohamed;S. Chakravorty;R. Goyal;Ran Wang
我们考虑了非线性随机最优控制问题。由于贝尔曼的“维度诅咒”，这个问题被认为是从根本上难以解决的。我们给出的结果表明，类似于模型预测控制，从当前状态重复求解开环确定性问题，得到的反馈策略接近于真正的全局随机最优策略，即O(ϵ4)。此外，经验结果表明，求解随机动态规划(DP)问题即使在易于处理的情况下也非常容易受到噪声的影响，并且在实践中，即使对于随机系统，MPC型反馈律也具有优越的性能。
We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman’s "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop deterministic problem from the current state, similar to Model Predictive Control (MPC), results in a feedback policy that is O(ϵ4) near to the true global stochastic optimal policy. Furthermore, empirical results show that solving the Stochastic Dynamic Programming (DP) problem is highly susceptible to noise, even when tractable, and in practice, the MPC-type feedback law offers superior performance even for stochastic systems.