Stabilisation for cascade of nonlinear ODEs and counter-convecting transport dynamics

We consider stabilisation for a nonlinear ordinary differential equation (ODE) and counter-convecting transport partial differential equations (PDEs) cascaded system in which the transport coefficients depend on the ODE state. Stability analysis of the closed-loop system is based on the infinite-dim...

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Bibliographic Details
Published in:International journal of systems science 2019-07, Vol.50 (10), p.2053-2062
Main Authors: Cai, Xiushan, Wang, Dingchao, Liu, Yang, Zhan, Xisheng, Yan, Huaicheng
Format: Article
Language:English
Subjects:
backstepping transformations
Cascaded system
Closed loop systems
counter-convecting transport dynamics
Dimensional stability
Feedback control
Ordinary differential equations
Partial differential equations
predictor control
Stability analysis
Transport properties
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Summary:We consider stabilisation for a nonlinear ordinary differential equation (ODE) and counter-convecting transport partial differential equations (PDEs) cascaded system in which the transport coefficients depend on the ODE state. Stability analysis of the closed-loop system is based on the infinite-dimensional backstepping transformations and a Lyapunov functional. A predictor control is proposed such that the closed-loop system is globally asymptotically stable. The proposed design method is illustrated by a single-link manipulator.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2019.1646350