Online convex programming and regularization in adaptive control

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2010, Pages 1957-1962

  Raginsky, Maxim ^a   Rakhlin, Alexander ^b   Yüksel, Serdar ^c  

^a USA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING; CONVEX OPTIMIZATION; COST FUNCTIONS; DECISION MAKING;

ADAPTIVE CONTROL SCHEMES; CONVEX COST FUNCTION; OPTIMAL PERFORMANCE; OUTPUT PREDICTION ERRORS; RECURSIVE PARAMETERS; SEQUENTIAL DECISION MAKING; SUPERVISORY CONTROLLERS; TIME VARYING UNCERTAINTIES;

ADAPTIVE CONTROL SYSTEMS;

EID: 79953129842     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2010.5717262     Document Type: Conference Paper

References (23)

1. G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984.
2. J. P. Hespanha, D. Liberzon, and A. S. Morse, "Hysteresis-based switching algorithms for supervisory control of uncertain systems," Automatica, vol. 39, pp. 263-272, 2003.
3. S. R. Kulkarni and P. J. Ramadge, "Model and controller selection policies based on output prediction errors," IEEE Trans. Automat. Control, vol. 41, no. 11, pp. 1594-1604, 1996.
4. A. S. Nemirovski and D. B. Yudin, Problem Complexity and Method Efficiency in Optimization. Wiley, 1983.
5. A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro, "Robust stochastic approximation approach to stochastic programming," SIAM J. Optim., vol. 19, no. 4, pp. 1574-1609, 2009.
6. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
7. Y. Wang and S. Boyd, "Fast model predictive control using online optimization," IEEE Trans. Control Sys. Technol., vol. 18, no. 2, pp. 267-278, 2010.
8. A. Beck and M. Teboulle, "Mirror descent and nonlinear projected subgradient methods for convex optimization," Operations Res. Lett., vol. 31, pp. 167-175, 2003.
9. M. Zinkevich, "Online convex programming and generalized infinitesimal gradient descent," in Proc. Int. Conf. on Machine Learning, 2003, pp. 928-936.
10. J. Hannan, "Approximation to Bayes risk in repeated play," Contributions to the Theory of Games, vol. 3, pp. 97-139, 1957.
11. L. M. Bregman, "The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming," USSR Comput. Math. and Math. Phys., vol. 7, pp. 200-217, 1967.
12. P. R. Kumar and P. Varaiya, Stochastic Systems: Estimation, Identification, and Adaptive Control. Prentice-Hall, 1986.
13. G. C. Goodwin, P. J. Ramadge, and P. E. Caines, "Discrete time stochastic adaptive control," SIAM J. Control Optim., vol. 19, no. 6, pp. 829-853, 1981.
14. M. Duflo, Random Iterative Models, ser. Applications of Mathematics. Springer, 1997, vol. 34.
15. L. Ljung, "Analysis of recursive stochastic algorithms," IEEE Trans. Automat. Control, vol. AC-22, no. 4, pp. 551-575, 1977.
16. N. Cesa-Bianchi and G. Lugosi, Prediction, Learning, and Games. Cambridge, 2006.
17. P. L. Bartlett, E. Hazan, and A. Rakhlin, "Adaptive online gradient descent," in Advances in Neural Information Processing Systems 20, 2007.
18. E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed. New York: Springer, 1998.
19. D. F. Delchamps, "Analytic feedback control and the algebraic Riccati equation," IEEE Trans. Automat. Control, vol. AC-29, pp. 1031-1033, 1984.
20. J. P. Hespanha and A. S. Morse, "Stability of switched systems with average dwell-time," in Proc. 38th IEEE Conf. on Decision and Control, Phoenix, AZ, 1999, pp. 2655-2660.
21. K. S. Narendra and J. Balakrishnan, "Adaptive control using multiple models," IEEE Trans. Automat. Control, vol. 42, no. 2, pp. 171-187, 1997.
22. J. Abernethy, E. Hazan, and A. Rakhlin, "Competing in the dark: An ffficient algorithm for bandit linear optimization," in Proc. 21st Annual Conf. on Learning Theory (COLT), 2008.
23. D. P. De Farias and N. Megiddo, "Combining expert advice in reactive environments," J. Assoc. Comput. Mach., vol. 53, no. 5, pp. 762-799, 2006.