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RESEARCH PAPERS

Functional Persistence of Excitation and Observability for Learning Control Systems

[+] Author and Article Information
J. B. Moore

Department of Systems Engineering, Australian National University, Canberra, Australia

R. Horowitz, W. Messner

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 114(3), 500-507 (Sep 01, 1992) (8 pages) doi:10.1115/1.2897375 History: Received October 17, 1990; Revised June 14, 1991; Online March 17, 2008

Abstract

Adaptive systems involving function learning can be formulated in terms of integral equations of the first kind, possibly with separable, finite-dimensional kernels. The learning process involves estimating the influence functions (Messner et al., 1989). To achieve convergence of the influence function estimates and exponentially stability, it is important to have persistence of excitation in the training tasks. This paper develops the concept of functional persistence of excitation (PE), and the associated concept of functional uniform complete observability (UCO). Relevant PE and UCO properties for linear systems are developed. For example, a key result is that uniform complete observability in this context is maintained under bounded integral operator output injection—a natural generalization of the corresponding finite dimensional result. This paper also demonstrates the application of the theory to linear error equations associated with a repetitive control algorithm.

Copyright © 1992 by The American Society of Mechanical Engineers
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