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IMA Journal of Mathematical Control and Information 1991 8(4):389-395; doi:10.1093/imamci/8.4.389
© 1991 by Institute of Mathematics and its Applications
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A Note on the Problem of Multivariable Adaptive Tracking

S. TOWNLEY and D.H. OWENS

University of Exeter, Department of Mathematics North Park Road, Exeter EX4 4QF, U.K.
University of Exeter, Centre for Systems and Control Engineering, School of Engineering North Park Road, Exeter EX4 4QF, U.K.

In this note we consider the problem of adaptive tracking for multivariable relative degree one, minimum phase systems. Our approach is in the spirit of Helmke et al. (1990) who considered adaptive tracking of sinusoidal reference signals for single-input, single-output systems. The case of relative degree r, single-input, single-output, minimum-phase systems has been considered in Mareels (1984). The main contribution we make is in establishing that the sufficient conditions for universal adaptive tracking, namely minimum phase, relative degree one and the internal model principle, hold for the suitably precompensated plant. This enables us to apply the techniques of Helmke et al. (1990).


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