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

2006

Conference Paper

ei


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.

Author(s): Deisenroth, MP. and Ohtsuka, T. and Weissel, F. and Brunn, D. and Hanebeck, UD.
Book Title: MFI 2006
Journal: Proceedings of the 6th IEEE International Conference on Multisensor Fusion and Integration (MFI 2006)
Pages: 371-376
Year: 2006
Month: September
Day: 0
Editors: Hanebeck, U. D.
Publisher: IEEE Service Center

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1109/MFI.2006.265616
Event Name: 6th IEEE International Conference on Multisensor Fusion and Integration
Event Place: Heidelberg, Germany

Address: Piscataway, NJ, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{4185,
  title = {Finite-Horizon Optimal State-Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle},
  author = {Deisenroth, MP. and Ohtsuka, T. and Weissel, F. and Brunn, D. and Hanebeck, UD.},
  journal = {Proceedings of the 6th IEEE International Conference on Multisensor Fusion and Integration (MFI 2006)},
  booktitle = {MFI 2006},
  pages = {371-376},
  editors = {Hanebeck, U. D.},
  publisher = {IEEE Service Center},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Piscataway, NJ, USA},
  month = sep,
  year = {2006},
  month_numeric = {9}
}