论文标题
关于随机最佳非线性控制的反馈定律
On the Feedback Law in Stochastic Optimal Nonlinear Control
论文作者
论文摘要
We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's "curse of dimensionality".我们提出了一个结果表明，从当前状态中反复求解逐渐短的视野，类似于模型预测性控制（MPC），导致反馈策略是$ O（ε^4）$靠近真正的全局全局最佳最佳策略，其中$ε$是扰动参数模块的噪声。我们还表明，最佳的确定性反馈问题具有扰动结构，因此反馈定律的高阶项不会影响低阶项，并且在最佳随机反馈问题中丢失了这种结构。因此，即使在低维问题中，解决随机动态编程问题也非常容易受到噪声的影响，而实际上，MPC型反馈定律即使对于高噪声水平也提供了卓越的性能。
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 with progressively shorter horizons, similar to Model Predictive Control (MPC), results in a feedback policy that is $O(ε^4)$ near to the true global stochastic optimal policy, where $ε$ is a perturbation parameter modulating the noise. We also show that the optimal deterministic feedback problem has a perturbation structure such that higher-order terms of the feedback law do not affect lower-order terms and that this structure is lost in the optimal stochastic feedback problem. Consequently, solving the Stochastic Dynamic Programming problem is highly susceptible to noise, even in low dimensional problems, and in practice, the MPC-type feedback law offers superior performance even for high noise levels.
