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

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##### Citation

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.* Proceedings
of the 6th IEEE International Conference on Multisensor Fusion and Integration (MFI 2006),* 371-376.

Cite as: http://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.