On the concept of excitation in least squares identification and adaptive control†
- 1 March 1986
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 16 (3-4) , 227-254
- https://doi.org/10.1080/17442508608833375
Abstract
Making use of martingale theory, stochastic regression theory, and certain properties of matrix polynomials in the unit shift operator, we study the problem concerning how much excitation should be introduced into the inputs in a multivariable ARMAX system for (i) consistent estimation of the system parameters by the method of extended least squares, and (ii) asymptotically efficient adaptive regulation of the system by using a perturbed version of the classical self-tuning regulator. In this connection, it is shown how the classical persistency-of-excitation-type conditions on regression vectors of past inputs, outputs and noise terms can be translated into corresponding conditions involving the inputs alone. Moreover, much weaker types of excitation conditions than persistent excitation are introduced and studied.Keywords
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