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

Deisenroth, MP; Ohtsuka, T; Weissel, F; Brunn, D; Hanebeck, UD

doi:10.1109/MFI.2006.265616

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

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Deisenroth, M., Ohtsuka, T., Weissel, F., Brunn, D., & Hanebeck, U. (2006). Finite-Horizon Optimal State-Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle. In U. Hanebeck (Ed.), 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (pp. 371-376). Piscataway, NJ, USA: IEEE Service Center.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-D045-E

Abstract

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.