Stabilité des algorithmes récursifs d’adaptation

AnalyseLes analyses de stabilité et de convergence, réalisées tant dans un environnement déterministe que stochastique sont restées longtemps incomplètes, voire inexistantes. Les auteurs présentent un aperçu des résultats obtenus à ce jour, concernant la stabilité et la convergence des algorithmes récursifs d’adaptation. Ils donnent également quelques exemples à travers des schémas d’identification.AbstractStability and convergence analysis remained incomplete or even non-existant as much in a deterministic environment as in a stochastic one. The authors intend to give an overview of results obtained till now, concerning the stability and convergence analysis of adaptive recursive algorithms. They also give some examples with the help of identification schemes.

[1]  David C. Farden Stochastic approximation with correlated data , 1981, IEEE Trans. Inf. Theory.

[2]  V. Solo The convergence of AML , 1979 .

[3]  I. Landau,et al.  Elimination of the real positivity condition in the design of parallel MRAS , 1978 .

[4]  I. Landau,et al.  Near supermartingales for convergence analysis of recursive identification and adaptive control schemes , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[5]  J. Fuchs Discrete adaptive control: A sufficient condition for stability and applications , 1980 .

[6]  I. Landau An extension of a stability theorem applicable to adaptive control , 1980 .

[7]  L. Dugard,et al.  Stochastic model reference adaptive controllers , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[8]  David Falconer Adaptive filter theory and applications , 1980 .

[9]  I. Landau Unbiased recursive identification using model reference adaptive techniques , 1976 .

[10]  Rogelio Lozano,et al.  Redesign of explicit and implicit discrete time model reference adaptive control schemes , 1981 .

[11]  P. Ramadge,et al.  Discrete-time multivariable adaptive control , 1979 .

[12]  Lennart Ljung,et al.  Analysis of recursive stochastic algorithms , 1977 .

[13]  K. Narendra,et al.  Stable adaptive controller design, part II: Proof of stability , 1980 .

[14]  Emil Geles,et al.  L'hyperstabilité des systèmes automatiques , 1973 .