A new adaptive control algorithm for systems with multilinear parametrization

Netto, Mariana; Annaswamy, Anuradha M.; Mammar, Saïd; Glaser, Sébastien

doi:10.1109/acc.2006.1657361

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…In [24] reparametrization to convexify an otherwise non-convexly parameterized system is proposed. See also [25] and [35] for some interesting results along these lines, where the controller and the estimator switch between over/underbounding convex/concave functions.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Parameter Estimation of Nonlinearly Parameterized Regressions without Overparameterization nor Persistent Excitation: Application to System Identification and Adaptive Control

Gromov¹,

Nuño²,

Pyrkin³

et al. 2019

Preprint

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In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions-continuous or discrete time-and apply it for system identification and adaptive control. We restrict our attention to parameterizations that can be factorized as the product of two functions, a measurable one and a nonlinear function of the parameters to be estimated. Although in this case it is possible to define an extended vector of unknown parameters to get a linear regression, it is well-known that overparameterization suffers from some severe shortcomings. Another feature of the proposed estimator is that parameter convergence is ensured without a persistency of excitation assumption. It is assumed that, after a coordinate change, some of the elements of the transformed function satisfy a monotonicity condition. The proposed estimators are applied to design identifiers and adaptive controllers for nonlinearly parameterized systems. In continuous-time we consider a general class of nonlinear systems and those described by Euler-Lagrange models, while in discrete-time we apply the method to the challenging problems of direct and indirect adaptive pole-placement. The effectiveness of our approach is illustrated with several classical examples, which are traditionally tackled using overparameterization and assuming persistency of excitation.

show abstract

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Parameter Estimation of Nonlinearly Parameterized Regressions without Overparameterization nor Persistent Excitation: Application to System Identification and Adaptive Control

Gromov¹,

Nuño²,

Pyrkin³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In Netto et al [2000] reparametrization to convexify an otherwise non-convexly parameterized system is proposed. See also Netto et al [2006] and Tyukin et al [2003] for some recent interesting results along these lines, where the controller and the estimator switch between over/underbounding convex/concave functions. Similarly to the present paper, in Tyukin et al [2007] monotonicity, instead of convexity, is used-but under radically different assumptions.…”

Section: Introductionmentioning

confidence: 99%