TY - JOUR

T1 - Asymptotic Tracking and Linear-like Behavior Using Multi-Model Adaptive Control

AU - Shahab, Mohamad T.

AU - Miller, Daniel E.

N1 - KAUST Repository Item: Exported on 2021-01-26
Acknowledgements: This research is supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC).

PY - 2021

Y1 - 2021

N2 - In 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.

AB - In 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.

UR - http://hdl.handle.net/10754/666923

UR - https://ieeexplore.ieee.org/document/9328271/

U2 - 10.1109/TAC.2021.3052745

DO - 10.1109/TAC.2021.3052745

M3 - Article

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 2334-3303

ER -