Adaptive optimization and D-optimum experimental design

Annals of Statistics

Volumn 28, Issue 6, 2000, Pages 1743-1761

  Pronzato, Luc ^a  

^a UNIVERSITY OF NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Adaptive control; D optimum design; Least squares estimation; Sequential design; Strong consistency

Indexed keywords

EID: 0034343448     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015957479     Document Type: Article

References (25)

1. ALLISON, B. J., TESSIER, P. J. C. and DUMONT, G. A. (1995). Comparison of suboptimal dual adaptive controllers. In Proceedings of the 3rd European Control Conference 36-43. Rome.
2. ALSTER, J. and BLANGER, P. R. (1974). A technique for dual adaptive control. Automatica 10 627-634.
3. ASTRÖM, K. J. and WITTENMARK, B. (1989). Adaptive Control. Addison-Wesley, Reading, MA.
4. BAR-SHALOM, Y. (1981). Stochastic dynamic programming: caution and probing. IEEE Trans. Automatic Control 26 1184-1195.
5. BAR-SHALOM, Y. and TSE, E. (1974). Dual effect, certainty equivalence, and separation in stochastic control. IEEE Trans. Automatic Control 19 494-500.
6. BOZIN, A. S. and ZARROP, M. B. (1991). Self tuning optimizer-convergence and robustness properties. In Proceedings of the 1st European Control Conference 672-677. Hermés, Paris.
7. FEL'DBAUM, A. A. (1960a). Dual control theory. I. Automat. i Telemek. 21 1240-1249.
8. FEL'DBAUM, A. A. (1960b). Dual control theory. II. Automat. i Telemek. 21 1453-1464.
9. FEL'DBAUM, A. A. (1961a). The theory of dual control. III. Automat. i Telemek. 22 3-16.
10. FEL'DBAUM, A. A. (1961b). The theory of dual control. IV. Automat. i Telemek. 22 129-142.
11. GINEBRA, J. and CLAYTON, M. K. (1995). Response surface bandits. J. Roy. Statist. Soc. Ser. B 771-784.
12. KULCSÁR, C., PRONZATO, L. and WALTER, E. (1996). Dual control of linearly parameterised models via prediction of posterior densities. European J. Control 2 135-143.
13. LAI, T. L. and WEI, C. Z. (1982). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10 154-166.
14. LAI, T. L. and WEI, C. Z. (1987). Asymptotically efficient self-tuning regulators. SIAM J. Control Optim. 25 466-481.
15. LJUNG, L. (1977). Analysis of recursive stochastic algorithms. IEEE Trans. Automat. Control 22 551-575.
16. PÁZMAN, A. (1974). A convergence theorem in the theory of D-optimum experimental designs. Ann. Statist. 2 216-218.
17. PÁZMAN, A. (1986). Foundations of Optimum Experimental Design. Reidel, Dordrecht.
18. PRONZATO, L. and WALTER, E. (1993). Experimental design for estimating the optimum point in a response surface. Acta Appl. Math. 33 45-68.
19. PUKELSHEIM, F. (1993). Optimal Experimental Design. Wiley, New York.
20. SILVEY, S. D. (1980). Optimal Design. Chapman & Hall, London.
21. WELLSTEAD, P. E. and ZARROP, M. B. (1991). Self-Tuning Sytems. Wiley, Chichester.
22. WITTENMARK, B. (1975). An active suboptimal controller for systems with stochastic parameters. Automat. Control Theory Appl. 3 13-19.
23. WITTENMARK, B. and ELEVITCH, C. (1985). An adaptive control algorithm with dual features. In Prep. 7th IFAC/IFORS Symposium on Identification and System Parameter Estimation 587-592, York.
24. WU, C.-F. and WYNN, H. P. (1978). The convergence of general step-length algorithms for regular optimum design criteria. Ann. Statist. 6 1273-1285.
25. WYNN, H.P. (1970). The sequential generation of D-optimum experimental designs. Ann. Math. Statist. 41 1655-1664.