Near Optimality and Tractability in Stochastic Nonlinear Control

04/01/2020

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by   Mohamed Naveed Gul Mohamed, et al.

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We consider the problem of nonlinear stochastic optimal control. This is fundamentally intractable owing to Bellman's infamous "curse of dimensionality". We present a "decoupling principle" for the tractable feedback design for such problems, wherein, first, a nominal open-loop problem is solved, followed by a suitable linear feedback design around the open-loop. The performance of the resulting feedback law is shown to be asymptotically close to the true stochastic feedback law to fourth order in a small noise parameter ϵ. The decoupling theory is empirically tested on robotic planning problems under uncertainty.