Will the self-tuning approach work for general cost criteria?

We expose a fundamental limitation of the self-tuning procedure for adaptive control of linear stochastic systems. Specifically, if the cost criterion measuring the performance of the unknown system is anything other than a minimum (output) variance criterion, then the procedure of estimating the un...

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Bibliographic Details
Published in:Systems & control letters 1985-01, Vol.6 (2), p.77-85
Main Authors: Lin, Woei, Kumar, P.R., Seidman, T.I.
Format: Article
Language:English
Subjects:
Adaptative systems
Adaptive control
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Self-tuning
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Summary:We expose a fundamental limitation of the self-tuning procedure for adaptive control of linear stochastic systems. Specifically, if the cost criterion measuring the performance of the unknown system is anything other than a minimum (output) variance criterion, then the procedure of estimating the unknown parameters of the linear system and then applying a control input which is optimal for the given cost criterion and the parameter estimates, will not self-tune to the optimal control law. Since our arguments are based on the analysis of an ordinary differential equation of Ljung, and since we do not, in our general context, have a proof that this O.D.E. represents the asymptotic behaviour of the system, further work is needed. An exception to the above situation is the class of systems with a large enough delay, for which self-tuning to the optimal, and indeed, convergence to the true parameters, cannot be ruled out.
ISSN:0167-6911
1872-7956
DOI:10.1016/0167-6911(85)90001-5