A CLOSED-FORM MODEL PREDICTIVE CONTROL FRAMEWORK FOR NONLINEAR NOISE-CORRUPTED SYSTEMS

Florian Weissel, Marco F. Huber, Uwe D. Hanebeck

Abstract

In this paper, a framework for Nonlinear Model Predictive Control (NMPC) that explicitly incorporates the noise influence on systems with continuous state spaces is introduced. By the incorporation of noise, which results from uncertainties during model identification and the measurement process, the quality of control can be significantly increased. Since NMPC requires the prediction of system states over a certain horizon, an efficient state prediction technique for nonlinear noise-affected systems is required. This is achieved by using transition densities approximated by axis-aligned Gaussian mixtures together with methods to reduce the computational burden. A versatile cost function representation also employing Gaussian mixtures provides an increased freedom of modeling. Combining the prediction technique with this value function representation allows closed-form calculation of the necessary optimization problems arising from NMPC. The capabilities of the framework and especially the benefits that can be gained by considering the noise in the controller are illustrated by the example of a mobile robot following a given path.

References

  1. Bertsekas, D. P. (2000). Dynamic Programming and Optimal Control. Athena Scientific, Belmont, Massachusetts, U.S.A., 2nd edition.
  2. Camacho, E. F. and Bordons, C. (2004). Model Predictive Control. Springer-Verlag London Ltd., 2 edition.
  3. Deisenroth, M. P., Ohtsuka, T., Weissel, F., Brunn, D., and Hanebeck., U. D. (2006). Finite-Horizon Optimal State Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle. In Proc. of the IEEE Int. Conf. on Multisensor Fusion and Integration for Intelligent Systems, pages 371-376.
  4. Findeisen, R. and Allgöwer, F. (2002). An Introduction to Nonlinear Model Predictive Control. In Scherer, C. and Schumacher, J., editors, Summerschool on ”The Impact of Optimization in Control”, Dutch Institute of Systems and Control (DISC), pages 3.1-3.45.
  5. de Freitas, N. (2002). Rao-Blackwellised Particle Filtering for Fault Diagnosis. In IEEE Aerospace Conference Proceedings, volume 4, pages 1767-1772.
  6. He, Y. and Chong, E. K. P. (2004). Sensor Scheduling for Target Tracking in Sensor Networks. In Proceedings of the 43rd IEEE Conference on Decision and Control, volume 1, pages 743-748.
  7. Huber, M., Brunn, D., and Hanebeck, U. D. (2006). ClosedForm Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density. In Proc. of the IEEE Int. Conf. on Multisensor Fusion and Integration for Intelligent Systems, pages 98-103.
  8. Kalman, R. E. (1960). A new Approach to Linear Filtering and Prediction Problems. Transactions of the ASME, Journal of Basic Engineering, (82):35-45.
  9. Lee, J. H. and Ricker, N. L. (1994). Extended Kalman Filter Based Nonlinear Model Predictive Control. In Industrial & Engineering Chemistry Research, pages 1530- 1541. ACS.
  10. Lincoln, B. and Rantzer, A. (2006). Relaxing Dynamic Programming. IEEE Transactions on Automatic Control, 51(8):1249-1260.
  11. Maz'ya, V. and Schmidt, G. (1996). On Approximate Approximations using Gaussian Kernels. IMA Journal of Numerical Analysis, 16(1):13-29.
  12. Nikovski, D. and Brand, M. (2003). Non-Linear Stochastic Control in Continuous State Spaces by Exact Integration in Bellman's Equations. In Proc. of the 2003 International Conf. on Automated Planning and Scheduling, pages 91-95.
  13. Ohtsuka, T. (2003). A Continuation/GMRES Method for Fast Computation of Nonlinear Receding Horizon Control. Automatica, 40(4):563-574.
  14. Qin, S. J. and Badgewell, T. A. (1997). An Overview of Industrial Model Predictive Control Technology. Chemical Process Control, 93:232-256.
  15. Schweppe, F. C. (1973). Uncertain Dynamic Systems. Prentice-Hall.
Download


Paper Citation


in Harvard Style

Weissel F., F. Huber M. and D. Hanebeck U. (2007). A CLOSED-FORM MODEL PREDICTIVE CONTROL FRAMEWORK FOR NONLINEAR NOISE-CORRUPTED SYSTEMS . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-972-8865-84-9, pages 62-69. DOI: 10.5220/0001625500620069


in Bibtex Style

@conference{icinco07,
author={Florian Weissel and Marco F. Huber and Uwe D. Hanebeck},
title={A CLOSED-FORM MODEL PREDICTIVE CONTROL FRAMEWORK FOR NONLINEAR NOISE-CORRUPTED SYSTEMS},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2007},
pages={62-69},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001625500620069},
isbn={978-972-8865-84-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - A CLOSED-FORM MODEL PREDICTIVE CONTROL FRAMEWORK FOR NONLINEAR NOISE-CORRUPTED SYSTEMS
SN - 978-972-8865-84-9
AU - Weissel F.
AU - F. Huber M.
AU - D. Hanebeck U.
PY - 2007
SP - 62
EP - 69
DO - 10.5220/0001625500620069