Asymptotic Tracking and Linear-like Behavior Using Multi-Model Adaptive Control
KAUST DepartmentDepartment of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada, and is with the Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, King Abdullah University of Science & Technology (KAUST), Thuwal 23955, Saudi Arabia.
Permanent link to this recordhttp://hdl.handle.net/10754/666923
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AbstractIn this paper, we consider the problem of tracking for a discrete-time plant with unknown plant parameters; we assume knowledge of an upper bound on the plant order, and for each admissible order we assume knowledge of a compact set in which the plant parameters lie. We carry out parameter estimation of an associated auxiliary model; indeed, for each admissible dimension, we cover the set of admissible parameters by a finite number of compact and convex sets and use an original-projection-algorithm-based estimator for each set. At each point in time, we employ a switching algorithm to determine which model and parameter estimates are used in the pole-placement-based control law. We prove that this adaptive controller guarantees desirable linear-like closed-loop behavior: exponential stability, a bounded noise gain in every p-norm, a convolution bound on the effect of the exogenous inputs, as well as exponential tracking for certain classes of reference and noise signals; this linear-like behavior is leveraged to immediately show tolerance to a degree of plant time-variations and unmodelled dynamics.
SponsorsThis research is supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC).