Explicit stochastic nonlinear predictive control based on Gaussian process models

2007 European Control Conference, ECC 2007

Volumn , Issue , 2007, Pages 2340-2347

  Grancharova, Alexandra ^a   Kocijan, Jus ^b   Johansen, Tor A ^c  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

^b JO EF STEFAN INSTITUTE   (Slovenia)

^c NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); MODEL PREDICTIVE CONTROL; NONLINEAR PROGRAMMING; NONLINEAR SYSTEMS; PREDICTIVE CONTROL SYSTEMS; STOCHASTIC SYSTEMS; TREES (MATHEMATICS);

CONSTRAINED NONLINEAR SYSTEMS; GAUSSIAN PROCESS MODELS; NONLINEAR MODEL PREDICTIVE CONTROL; NONLINEAR PREDICTIVE CONTROL; ONLINE COMPUTATIONS; ONLINE OPTIMIZATION; PREDICTION UNCERTAINTY; STATE SPACE PARTITIONS;

STOCHASTIC MODELS;

EID: 84927739705     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2007.7068422     Document Type: Conference Paper

References (28)

1. S. S. Keerthi and E. G. Gilbert, "Optimal infinite horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving horizon approximations", Journal of Optimization Theory and Applications, vol. 57, pp. 265-293, 1988.
2. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality", Automatica, vol. 36, pp. 789-814, 2000.
3. F. Allgöwer and A. Zheng (eds.), Nonlinear Model Predictive Control, Progress in system and control theory, Vol. 26, Birkhäuser Verlag, Basel, 2000.
4. B. Kouvaritakis and M. Cannon (eds.), Nonlinear predictive control, Theory and practice, IEE Control Engineering Series 61, IEE, 2001.
5. L. Magni and R. Scattolini, "Stabilizing model predictive control of nonlinear continuous time systems", Annual Reviews in Control, vol. 28, pp. 1-11, 2004.
6. J. H. Lee and B. L. Cooley, "Optimal feedback control strategies for state-space systems with stochastic parameters", IEEE Transactions on Automatic Control, vol. 43, No. 10, pp. 1469-1475, 1998.
7. D. van Hessem, C. W. Scherer, and O. H. Bosgra, "LMI-based closed-loop economic optimization of stochastic process operation under state and input constraints. Proceedings of the 40-th IEEE Conference on Decision and Control, 2001, pp. 4228-4233.
8. J. Yan and R. R. Bitmead, "Incorporating state estimation into model predictive control and its application to network traffic control", Automatica, vol. 41, pp. 595-604, 2005.
9. B. Kouvaritakis, M. Cannon, and P. Couchman, "MPC as a tool for sustainable development integrated policy assessment", IEEE Transactions on Automatic Control, vol. 51, No. 1, pp. 145-149, 2006.
10. P. Couchman, B. Kouvaritakis, and M. Cannon, "LTV models in MPC for sustainable development", International Journal of Control, vol. 79, No. 1, pp. 63-73, 2006.
11. P. Couchman, M. Cannon, and B. Kouvaritakis, "Stochastic MPC with inequality stability constraints", Automatica, vol. 42, No. 12, pp. 2169-2174, 2006.
12. P. Couchman, M. Cannon, and B. Kouvaritakis, "MPC for stochastic systems", Proceedings of the International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, Freudenstadt-Lauterbad, Germany, 26-30 August, 2005, pp. 61-72.
13. J. Kocijan, A. Girard, B. Banko, and R. Murray-Smith, "Dynamic systems identification with Gaussian processes", Mathematical and Computer Modelling of Dynamic Systems, vol. 11, No. 4, pp. 411-424, 2005.
14. E. Solak, R. Murray-Smith, W. E. Leithead, D. J. Leith, and C. E. Rasmussen, "Derivative observations in Gaussian process models of dynamic systems", NIPS 15, Vancouver, Canada, MIT Press, 2003.
15. A. Girard, C. E. Rasmussen, J. Quinonero Candela, and R. Murray-Smith, "Gaussian process priors with uncertain inputs & application to multiple-step ahead time series forecasting", NIPS 15, Vancouver, Canada, MIT Press, 2003.
16. J. Kocijan, and R. Murray-Smith, "Non-linear predictive control with a Gaussian process model", In Switching and Learning in Feedback Systems, Eds. R. Shorten and R. Murray-Smith, Lecture Notes in Computer Science 3355, Springer-Verlag, Heidelberg, Germany, 2005.
17. B. Likar and J. Kocijan, "Predictive control of a gas-liquid separation plant based on a Gaussian process model", Computers & Chemical Engineering, vol. 31, pp. 142-152, 2007.
18. R. Murray-Smith, D. Sbarbaro, C. E. Rasmussen, and A. Girard, "Adaptive, cautious, predictive control with Gaussian process priors", Proceedings of 13-th IFAC Symposium on System Identification, Rotterdam, 2003.
19. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems". Automatica, vol. 38, pp. 3-20, 2002.
20. M. Bacic, M. Cannon, and B. Kouvaritakis, "Constrained NMPC via state-space partitioning for input-affine non-linear systems". Proceedings of American Control Conference, Denver, Colorado, 2003.
21. T. A. Johansen, "On multi-parametric nonlinear programming and explicit nonlinear model predictive control", Proceedings of IEEE Conference on Decision and Control, Las Vegas, NV, 2002, vol. 3, pp. 2768-2773.
22. T. A. Johansen, "Approximate explicit receding horizon control of constrained nonlinear systems", Automatica vol. 40, pp. 293-300, 2004.
23. A. Grancharova, T. A. Johansen, and P. Tøndel, "Computational aspects of approximate explicit nonlinear model predictive control", Proceedings of the International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, Freudenstadt-Lauterbad, Germany, 26-30 August, 2005, pp. 85-96.
24. A. V. Fiacco, Introduction to sensitivity and stability analysis in nonlinear programming. Orlando, Fl: Academic Press, 1983.
25. T. A. Johansen and A. Grancharova, "Approximate explicit constrained linear model predictive control via orthogonal search tree", IEEE Transactions on Automatic Control, vol. 48, pp. 810-815, 2003.
26. C. K. I. Williams, "Prediction with Gaussian processes: From linear regression to linear prediction and beyond", In Learning in Graphical Models, M. I. Jordan, (ed.), Kluwer Academic, Dordrecht, pp. 599-621, 1998.
27. C. E. Rasmussen, Evaluation of Gaussian Processes and other Methods for Non-Linear Regression, Ph. D. Disertation, Graduate department of Computer Science, University of Toronto, Toronto, 1996.
28. A. Girard and R. Murray-Smith, "Gaussian process: Prediction at a noisy input and application to iterative multiple-step ahead forecasting of time-series", In Switching and Learning in Feedback Systems, Eds. R. Shorten and R. Murray-Smith, Lecture Notes in Computer Science 3355, Springer-Verlag, Heidelberg, Germany, 2005.