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Finite-Horizon Optimal State-Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle

Deisenroth, Marc P.; Ohtsuka, Toshiyuki; Weissel, Florian; Brunn, Dietrich; Hanebeck, Uwe D.

In this paper, an approach to the finite-horizon optimal state-feedback control problem of nonlinear, stochastic, discrete-time systems is presented. Starting from the dynamic programming equation, the value function will be approximated by means of Taylor series expansion up to second-order
derivatives. Moreover, the problem will be reformulated, such that a minimum principle can be applied to the stochastic problem. Employing this minimum principle, the optimal control problem can be rewritten as a two-point boundary-value problem to be solved at each time step of a shrinking horizon.
To avoid numerical problems, the two-point boundary-value problem will be solved by means of a continuation method. Thus, the curse of dimensionality of dynamic programming is avoided, and good candidates for the optimal state-feedback controls are obtained. The proposed approach will be evaluated by means of a scalar example system.

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Volltext §
DOI: 10.5445/IR/1000013896
Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2006
Sprache Englisch
Identifikator ISBN: 1-424-40566-1
KITopen-ID: 1000013896
Erschienen in Proceedings / 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, 3 - 4 Sept. 200, Heidelberg, Germany
Verlag IEEE Service Center, Piscataway (NJ)
Seiten 371 - 376
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