RICCATI SOLUTION FOR DISCRETE STOCHASTIC SYSTEMS WITH STATE AND CONTROL DEPENDENT NOISE

Randa Herzallah

2009

Abstract

In this paper we present the Riccati solution of linear quadratic control problems with input and state dependent noise which is encountered during our previous study to the adaptive critic solution for systems characterized by functional uncertainty. Uncertainty of the system equations is quantified using a state and control dependent noise model. The derived optimal control law is shown to be of cautious type controllers. The derivation of the Riccati solution is via the principle of optimality. The Riccati solution is implemented to linear multi dimensional control problem and compared to the certainty equivalent Riccati solution.

References

  1. Anderson, B. D. O. and Moore, J. B. (1971). Linear Optimal Control. Prentice-Hall, Inc., Englewood Cliffs, N.J.
  2. Apley, D. (2004). A cautious minimum variance controller with ARIMA disturbances. IIE Transactions, 36(5):417-432.
  3. A° ström, K. J. and Wittenmark, B. (1989). Adaptive Control. Addison-Wesley, Reading, MA, U.S.A.
  4. Bellman, R. E. (1961). Adaptive Control Processes. Princeton University Press, Princeton, NJ.
  5. Bellman, R. E. (1962). Applied Dynamic Programming. Princeton University Press, Princeton, NJ.
  6. Campi, M. C. and Prandini, M. (2003). Randomized algorithms for the synthesis of cautious adaptive controllers. Systems and Control Letters, 49:21-36.
  7. Fabri, S. and Kadirkamanathan, V. (1998). Dual adaptive control of nonlinear stochastic systems using neural networks. Automatica, 34(2):245-253.
  8. Fel'dbaum, A. A. (1960). Dual control theory I-II. Automation and Remote Control, 21:874-880.
  9. Fel'dbaum, A. A. (1961). Dual control theory III-IV. Automation and Remote Control, 22:109-121.
  10. Filatov, N. M. and Unbehauen, H. (2000). Survey of adaptive dual control methods. IEE Proceedings Control Theory and Applications, 147:118-128.
  11. Gersho, A. and Gray, R. M. (1992). Vector Quantization and Signal Compression. Kluwer Academic Publishers.
  12. Goodwin, G. C. and Sin, K. S. (1984). Adaptive Filtering Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ.
  13. Guo, L. and Chen, H.-F. (1991). The A°ström-Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers. IEEE Transactions on Automatic Control, 36(7):802-812.
  14. Herzallah, R. (2007). Adaptive critic methods for stochastic systems with input-dependent noise. Automatica, 43(8):1355-1362.
  15. Herzallah, R. and Lowe, D. (2007). Distribution modeling of nonlinear inverse controllers under a Bayesian framework. IEEE Transactions on Neural Networks, 18:107-114.
  16. Maitelli, A. L. and Yoneyama, T. (1994). A two stage suboptimal controller for stochastic systems using approximate moments. Automatica, 30(12):1949-1954.
  17. Ogata, K. (1987). Discrete Time Control Systems. Prentice Hall, Inc., EnglewoodCliffs, New Jersey.
  18. Rami, M. A., Chen, X., Moore, J. B., and Zhou, X. Y. (2001). Solvability and asymptotic behavior of gneralized riccati equations arising in indefinite stochastic lq controls. IEEE Transactions on Automatic Control, 46(3):428-440.
  19. Xie, L. L. and Guo, L. (1998). Adaptive control of a class of discrete time affine nonlinear systems. Systems and Control Letters, 35:201-206.
  20. Yaz, E. (1986). Certainty equivalent control of stochastic sytems: Stability property. IEEE Transactions on Automatic Control, 31(2):178-180.
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Paper Citation


in Harvard Style

Herzallah R. (2009). RICCATI SOLUTION FOR DISCRETE STOCHASTIC SYSTEMS WITH STATE AND CONTROL DEPENDENT NOISE . In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-989-8111-99-9, pages 115-120. DOI: 10.5220/0002160501150120


in Bibtex Style

@conference{icinco09,
author={Randa Herzallah},
title={RICCATI SOLUTION FOR DISCRETE STOCHASTIC SYSTEMS WITH STATE AND CONTROL DEPENDENT NOISE},
booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2009},
pages={115-120},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002160501150120},
isbn={978-989-8111-99-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - RICCATI SOLUTION FOR DISCRETE STOCHASTIC SYSTEMS WITH STATE AND CONTROL DEPENDENT NOISE
SN - 978-989-8111-99-9
AU - Herzallah R.
PY - 2009
SP - 115
EP - 120
DO - 10.5220/0002160501150120