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On asymptotic model matching

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Abstract

In this paper we consider the problem of asymptotic model matching, in which the objective is to force the plant to behave asymptotically like a reference model in response to an exogenous input. Conditions for solvability via a linear time-invariant controller are well known; here we prove that under a closed-loop causality constraint, moving to a nonlinear time-varying controller affords no reduction of these conditions. We explore the ramifications of this result to the (ideal) model reference adaptive control problem, demonstrating that (i) an upper bound on the plant relative degreemust be known, and (ii) the plant zeros in the closed right half-planemust lie in a finite set. We also derive a bound on the achievable asymptotic performance in the event that the solvability conditions fail to hold.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Daniel E. Miller

  2. Department of Electrical Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    Edward J. Davison

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  1. Daniel E. Miller
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  2. Edward J. Davison
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Supported by the Natural Sciences and Engineering Research Council of Canada via a research grant.

Supported by the Natural Sciences and Engineering Research Council of Canada under Grant A4396.

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Miller, D.E., Davison, E.J. On asymptotic model matching. Math. Control Signal Systems 6, 322–340 (1993). https://doi.org/10.1007/BF01211500

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  • DOI: https://doi.org/10.1007/BF01211500

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