Overcoming the detectability obstacle in certainty equivalence adaptive control
type: Item
instance of: scholarly article
title: Overcoming the detectability obstacle in certainty equivalence adaptive control
zbMATH Open document ID: 1005.93043
DOI: 10.1016/S0005-1098(01)00305-3
author: Elena Panteley
author: Paloma Moya
author: Romeo Ortega
published in: Automatica
publication date: 2002-09-05T00:00:00Z
review text: This paper concerns global adaptive stabilization of nonlinear systems where both a linearly parameterized stabilizer and a Lyapunov function are known for the ideal closed-loop system. Although the standard estimator is implementable, the Lyapunov function is not assumed to be strict (i.e., with a derivative that is only negative semidefinite). The motivation behind this work derives from physical systems where the natural Lyapunov function is the total energy, which is not always strict. In prior work, completing the stability proof in these circumstances has required a rather restrictive detectability condition. Here, the authors take an alternate approach by adding to the parameter estimator an identification error coming from an incorrect identifier. The detectability assumption is then replaced by a new condition that requires that the negative definite terms in the Lyapunov function dominate.
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1797091
zbMATH Keywords: adaptive control
zbMATH Keywords: identification
zbMATH Keywords: nonlinear control
zbMATH Keywords: nonlinear systems
zbMATH Keywords: nonnegative definite Lyapunov function
zbMATH Keywords: global adaptive stabilization
zbMATH Keywords: detectability
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
cites work: Combined direct and indirect approach to adaptive control
cites work: Certainty equivalence implies detectability
cites work: Q3998946
cites work: Global stabilization of nonlinear cascade systems
cites work: Changing supply functions in input/state stable systems
cites work: A simple alternative to the Barbalat lemma
cites work: Integral characterizations of uniform asymptotic and exponential stability with applications
full work available at URL: s0005-1098(01)00305-3
OpenAlex ID: W2028376775
description: scientific article; zbMATH DE number 1797091