Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments

A strict Lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants, is presented. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the bounda...

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Published in:Automatica (Oxford) 2008-05, Vol.44 (5), p.1310-1318
Main Authors: Dos Santos, V., Bastin, G., Coron, J.-M., d’Andréa-Novel, B.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic
Automatic Control Engineering
Computer Science
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Engineering Sciences
Exact sciences and technology
Lyapunov stability
Riemann invariants
Saint-Venant equations
Systems of conservation laws
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cited_by cdi_FETCH-LOGICAL-c382t-3c34e508b592822da07b3b77654918e9e99059d26cebe20847f4d1e79201e8443
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creator Dos Santos, V.
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description A strict Lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants, is presented. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains. Previous stability results are extended to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state measured only at the boundaries. The control design method is illustrated with a hydraulic application, namely the level and flow regulation in a reach of the Sambre river and in the micro-channel of Valence, respectively through simulations and experimentations.
doi_str_mv 10.1016/j.automatica.2007.09.022
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subjects Applied sciences
Automatic
Automatic Control Engineering
Computer Science
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Engineering Sciences
Exact sciences and technology
Lyapunov stability
Riemann invariants
Saint-Venant equations
Systems of conservation laws
title Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments
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