Improved sample size bounds for probabilistic robust control design: A pack-based strategy

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 6178-6183

  Alamo, T ^a   Tempo, R ^b   Camacho, E F ^a  

^a UNIVERSIDAD DE SEVILLA   (Spain)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Probabilistic robustness; Randomized algorithms; Robust control; Robust convex optimization

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING; RANDOM PROCESSES;

PROBABILISTIC ROBUSTNESS; RANDOMIZED ALGORITHMS; ROBUST CONTROL DESIGN; ROBUST CONVEX OPTIMIZATION;

ROBUST CONTROL;

EID: 36749083615     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434615     Document Type: Conference Paper

References (18)

1. T. Alamo, R. Tempo, and E.F. Camacho. Revisiting statistical learning theory for uncertain feasibility and optimization problems. In Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, USA, December 2007.
2. T. Alamo, R. Tempo, and E.F. Camacho. Statistical learning theory: A pack-based strategy for uncertain feasibility and optimization problems. Technical Report, 2007.
3. T. Alamo, R. Tempo, D. Rodríguez, and E.F. Camacho. A sequentially optimal randomized algorithm for robust LMI feasibility problems. In Proceedings of the European Control Conference, 2007, Kos, Greece, July 2007.
4. V. D. Blondel and J.N. Tsitsiklis. A survey of computational complexity results in system and control. Automatica, 36:1249-1274, 2000.
5. G. Calafiore and M.C. Campi. Uncertain convex programs: randomized solutions and confidence levels. Math. Program, 102:25-46, 2005.
6. G. Calafiore and M.C. Campi. The scenario approach to robust control design. IEEE Transactions on Automatic Control, 51(5):742-753, 2006.
7. G. Calafiore and F. Dabbene. An iterative localization method for probabilistic feasibility of uncertain LMIs. In Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, USA, December 2006.
8. G. Calafiore and B.T. Polyak. Stochastic algorithms for exact and approximate feasibility of robust LMIs. IEEE Transactions on Automatic Control, 46(11): 1755-1759, 2001.
9. Y. Fujisaki, F. Dabbene, and R. Tempo. Probabilistic design of LPV control systems. Automatica, 39:1323-1337, 2003.
10. S. Kanev, B. De Schutter, and M. Verhaegen. An ellipsoid algorithm for probabilistic robust controller design. Systems and Control Letters, 49:365-375, 2003.
11. V. Koltchinskii, C.T. Abdallah, M. Ariola, P. Dorato, and D. Panchenko. Improved sample complexity estimates for statistical learning control of uncertain systems. IEEE Transactions on Automatic Control, 45(12):2383-2388, 2000.
12. B.T. Polyak and R. Tempo. Probabilistic robust design with linear quadratic regulators. Systems & Control Letters, 43:343-353, 2001.
13. R. Tempo, E.-W. Bai, and F. Dabbene. Probabilistic robustness analysis: Explicit bounds for the minimum number of samples. Systems & Control Letters, 30:237-242, 1997.
14. R. Tempo, G. Calafiore, and F. Dabbene. Randomized Algorithms for Analysis and Control of Uncertain Systems. Communications and Control Engineering Series. Springer-Verlag, London, 2005.
15. V.N. Vapnik. Statistical Learning Theory. John Wiley & Sons, New York, 1998.
16. M. Vidyasagar. A Theory of Learning and Generalization: with Applications to Neural Networks and Control Systems. Springer, London, 1997.
17. M. Vidyasagar. Statistical learning theory and randomized algorithms for control. Control Systems Magazine, 18(6):69-85, 1998.
18. M. Vidyasagar and V. D. Blondel. Probabilistic solutions to some NP-hard matrix problems. Automatica, 37(9): 1397-1405, 2001.