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Asymptotically efficient self-tuning regulators. (English) Zbl 0626.93034

The paper is concerned with the issue of convergence in self-tuning control.
In adaptive control, there is a conflicting requirement on the control input to provide on the one hand good output regulation and on the other hand sufficient excitation so as to provide reliable parameter estimates. The overall adaptive problem is difficult to solve, both computationally and analytically. A more practical approach is used in self-tuning control, where the control input is generated using the parameter estimates as if they were the true ones. The issue of convergence of such a scheme is then important.
The paper discusses how the dilemma between the need for information and the objective of efficient control can be resolved in the construction of asymptotically efficient self-tuning regulations by introducing white- noise probing inputs. The paper essentially derives a bound concerning the ‘regret’ (difference between the actual system output and the output for the known prameter case). The analysis is restricted to systems with white-noise disturbances.
Reviewer: A.Allidina

MSC:

93C40 Adaptive control/observation systems
62L20 Stochastic approximation
93E20 Optimal stochastic control
60G42 Martingales with discrete parameter
93E10 Estimation and detection in stochastic control theory
93E12 Identification in stochastic control theory
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