Brief Hysteresis-based switching algorithms for supervisory control of uncertain systems

Authors:
JoãO P. Hespanha;Daniel Liberzon;A.Stephen Morse
Affiliations:
Department of Electronical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA;Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;Department of Electrical Engineering, Yale University, New Haven, CT 06520, USA
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

We address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers. We present a new hysteresis-based switching logic, designed specifically for this purpose, and derive a bound on the number of switches produced by this logic on an arbitrary time interval. The resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics.