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

Mohamad T. Shahab, Daniel E. Miller

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
Pages (from-to)109691
JournalAutomatica
Volume130
DOIs
StatePublished - May 13 2021

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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