Observer design for a class of nonlinear system in cascade with counter-convecting transport dynamics

Cai, Xiushan; Liao, Linling; Zhang, Junfeng; Zhang, Wei

doi:10.14736/kyb-2016-1-0076

Cited by 5 publications

(11 citation statements)

References 20 publications

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“…Along this paper, the Euclidean norm of a vector X in R n and the respectively. Let H = R n × L 2 (0, l) the state space of the system (1)- (6). It is obvious that the vector space H equipped with its norm…”

Section: Problem Formulation and Main Resultsmentioning

confidence: 99%

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Exponential stabilization of cascade ODE-linearized KdV system by boundary Dirichlet actuation

Ayadi

2018

European Journal of Control

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In this paper, we solve the problem of exponential stabilization for a class of cascade ODE-PDE system governed by a linear ordinary differential equation and a 1 − d linearized Korteweg-de Vries equation (KdV) posed on a bounded interval. The control for the entire system acts on the left boundary with Dirichlet condition of the KdV equation whereas the KdV acts in the linear ODE by a Dirichlet connection. We use the socalled backstepping design in infinite dimension to convert the system under consideration into an exponentially stable cascade ODE-PDE system.Then, we use the invertibility of such design to achieve the exponential stability for the ODE-PDE cascade system under 2010 Mathematics Subject Classification. 93D05, 93D20, 34D05, 34D20.

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Section: Problem Formulation and Main Resultsmentioning

confidence: 99%

“…where the boundary conditions (4) and (6) has been used. Thus, from (17), (18), (20) and (22), for all λ > 0, the identity…”

Section: Control Designmentioning

confidence: 99%

Exponential stabilization of cascade ODE-linearized KdV system by boundary Dirichlet actuation

Ayadi

2018

European Journal of Control

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“…Remark In this work, to design a state feedback controller for the coupled system , we have selected the length l of the heat domain sufficiently small. Such a procedure is used in the observer design (which represents the dual problem of feedback design under consideration) for a globally Lipschitz nonlinear ODE in cascade with a heat equation in Reference . Contrarily to the cited article, in this work, we have only assumed that the nonlinear term is dominated by linear lower triangular structure, which is less conservative than the globally Lipschitz assumption.…”

Section: Well Posedness and Exponential Stabilizationmentioning

confidence: 99%

“…Many problems of stabilization for a class of linear coupled PDE‐ODE have been solved in References , , to name just a few. Some nonlinear extensions are studied in References where the nonlinear term is assumed to be globally Lipschitz, and in References for general nonlinear ODE.…”

Section: Introductionmentioning

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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“…Predictor-based techniques have been developed for stabilization linear/nonlinear systems with input delays [1,2,3,7,8,10,14,18], tracking control [26,27], optimal performance analysis of networked control systems [23,24,25], as well as observer design for a class of nonlinear system in cascade with counter-convecting transport dynamics [9].…”

Section: Introductionmentioning

confidence: 99%

Inverse optimal control for linearizable nonlinear systems with input delays

Cai¹,

Wu²,

Zhan³

et al. 2019

Kybernetika

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Observer design for a class of nonlinear system in cascade with counter-convecting transport dynamics

Cited by 5 publications

References 20 publications

Exponential stabilization of cascade ODE-linearized KdV system by boundary Dirichlet actuation

Exponential stabilization of cascade ODE-linearized KdV system by boundary Dirichlet actuation

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

Inverse optimal control for linearizable nonlinear systems with input delays

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