Adaptive output feedback regulation for a class of uncertain feedforward nonlinear systems

Benabdallah, Amel; Belfeki, Mohsen

doi:10.1002/acs.2703

Cited by 11 publications

(1 citation statement)

References 19 publications

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“…This is true when the nonlinear uncertain ODE is decoupled (ie, when B =0 and C =0). Furthermore, an adaptive output feedback that globally stabilizes more complicated class of uncertain nonlinear ODE is available in References , and .…”

Section: Resultsmentioning

confidence: 99%

Stabilization of a class of nonlinear uncertain ordinary differential equation by parabolic partial differential equation controller

Benabdallah

2020

Intl J Robust & Nonlinear

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This article is concerned with stabilization for a class of uncertain nonlinear ordinary differential equation (ODE) with dynamic controller governed by linear 1 − d heat partial differential equation (PDE). The control input acts at the one boundary of the heat's controller domain and the second boundary injects a Dirichlet term in ODE plant. The main contribution of this article is the use of the recent infinite-dimensional backstepping design for state feedback stabilization design of coupled PDE-ODE systems, to stabilize exponentially the nonlinear uncertain systems, under the restrictions that (a) the right-hand side of the ODE equation has the classical particular form: linear controllable part with an additive nonlinear uncertain function satisfying lower triangular linear growth condition, and (b) the length of the PDE domain has to be restricted. We solve the stabilization problem despite the fact that all known backstepping transformation in the literature cannot decouple the PDE and the ODE subsystems. Such difficulty is due to the presence of a nonlinear uncertain term in the ODE system. This is done by introducing a new globally exponentially stable target system for which the PDE and ODE subsystems are strongly coupled. Finally, an example is given to illustrate the design procedure of the proposed method. K E Y W O R D Sboundary stabilization, coupled partial differential equation-ordinary differential equation, infinite-dimensional backstepping, uncertain nonlinear system INTRODUCTIONIn the last decades, coupled partial differential equation (PDE)-ordinary differential equation (ODE) systems have attracted much attention in research communities because such systems can be used to model various processes such as road traffic, 1 gas flow pipeline, 2 power converters connected to transmission lines, 3 oil drilling, 4 and many other systems. The coupled PDE-ODE system considered in this article can be viewed as a perturbation of a simplified version that models the solid-gas interaction of heat diffusion and chemical reaction, where the interaction occurs at the interface. 5Abbreviations: ODE, ordinary differential equation; PDE, partial differential equation. Int J Robust Nonlinear Control. 2020;30:3023-3038. wileyonlinelibrary.com/journal/rnc

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Section: Resultsmentioning

confidence: 99%