Adaptive control of a class of discrete-time nonlinear systems yielding linear-like behavior

Embargo End Date
2023-05-13

Type
Article

Authors
Shahab, Mohamad T.
Miller, Daniel E.

KAUST Department
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Online Publication Date
2021-05-13

Print Publication Date
2021-08

Date
2021-05-13

Submitted Date
2020-05-10

Abstract
In adaptive control it is typically proven that an asymptotic form of stability holds, and that at best a bounded-noise bounded-state property is proven. Recently, however, it has been proven in a variety of scenarios that it is possible to carry out adaptive control for a linear time-invariant (LTI) discrete-time plant so that the closed-loop system enjoys linear-like behavior: exponential stability, a bounded noise gain, and a convolution bound on the exogenous signals; the key idea is to carry out parameter estimation by using the original projection algorithm together with restricting the parameter estimates to a convex set. In this paper, we extend this approach to a class of nonlinear plants and show how to carry out adaptive control so that we obtain the same desirable linear-like closed-loop properties. First, we consider plants with a known sign of the control gain; second, we consider the case when that sign is unknown, where two parameter estimators and a simple switching mechanism are used.

Citation
Shahab, M. T., & Miller, D. E. (2021). Adaptive control of a class of discrete-time nonlinear systems yielding linear-like behavior. Automatica, 130, 109691. doi:10.1016/j.automatica.2021.109691

Acknowledgements
Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Changyun Wen under the direction of Editor Miroslav Krstic.

Publisher
Elsevier BV

Journal
Automatica

DOI
10.1016/j.automatica.2021.109691

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S0005109821002119

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