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Stochastic Optimal Control of Nonlinear Systems via Short-Time Gaussian Approximation and Cell Mapping

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Abstract

A novel strategy to obtain global solutions of stochasticoptimal control problems with fixed state terminal conditions and controlbounds is proposed in this paper. The solution is global in the sense that theoptimal control solutions for all the initial conditions in a region of thestate space are obtained. The method makes use of Bellman's principle ofoptimality, the cumulant neglect closure method and the short-time Gaussianapproximation. A Markov chain with a control dependent transition probabilitymatrix is built using the generalized cell mapping method. This allows toevaluate the transient and steady state response of the controlled system. Themethod is applied to several linear and nonlinear systems leading to excellentcontrol performances.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Delaware, Newark, DE, 19716, U.S.A

    L. G. Crespo & J. Q. Sun

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  1. L. G. Crespo
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  2. J. Q. Sun
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Crespo, L.G., Sun, J.Q. Stochastic Optimal Control of Nonlinear Systems via Short-Time Gaussian Approximation and Cell Mapping. Nonlinear Dynamics 28, 323–342 (2002). https://doi.org/10.1023/A:1015600430713

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