Robustness of discrete-time direct adaptive controllers
- 1 December 1985
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 30 (12), 1179-1187
- https://doi.org/10.1109/tac.1985.1103890
Abstract
The problem of preserving stability of discrete-time adaptive controllers in spite of reduced-order modeling and output disturbances is addressed in this paper. Conditions for global stability (convergence of the tracking error with bounded signals) are derived for a discrete-time pole-zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals. Following an input-output perpective, the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors, respectively, and its stability is studied using the sector stability and passivity theorems. First the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure. In this L 2 -framework, it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed-loop transfer function verifies certain conicity conditions. The convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed. The results are further extended to a broader class of L_{\infty} disturbances and reference inputs.Keywords
This publication has 17 references indexed in Scilit:
- Robust adaptive control: Conditions for global stabilityIEEE Transactions on Automatic Control, 1985
- An input-output view of robustness in adaptive controlAutomatica, 1984
- Robustness enhancement of adaptive controllers by incorporation of process a priori knowledgeSystems & Control Letters, 1984
- Assessment of stability robustness for adaptive controllersIEEE Transactions on Automatic Control, 1983
- Bounded error adaptive controlIEEE Transactions on Automatic Control, 1982
- Robustness of self-tuning controllersIEE Proceedings D Control Theory and Applications, 1982
- Multivariable feedback design: Concepts for a classical/modern synthesisIEEE Transactions on Automatic Control, 1981
- On the stability and convergence of a self-tuning controllerInternational Journal of Control, 1980
- A stability theorem with applications to adaptive controlIEEE Transactions on Automatic Control, 1979
- Feedback Systems: Input-Output PropertiesJournal of Dynamic Systems, Measurement, and Control, 1975