An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems

Lamare, Pierre-Olivier; Girard, Antoine; Prieur, Christophe

doi:10.1051/cocv/2016038

Cited by 14 publications

(30 citation statements)

References 16 publications

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“…Note that the computation steps 3 to 4 could be replaced by using multiple linear matrix inequalities (LMI) instead of (9c), as suggested by the polytopic approach proposed by Lamare et al (2016).…”

Section: Simulation Resultsmentioning

confidence: 99%

PDE Observer Design for Counter-Current Heat Flows in a Heat-Exchanger

2017

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In this work, we consider the estimation of temperature profiles along the pipes of a plate heat exchanger. The transport phenomena through the heat exchanger are modeled by hyperbolic partial differential equations (PDE) of first order in time and space. The counterflow heat exchange implies that the system is comprised of rightward (where the hot fluid circulates) and leftward (cold fluid pipes) hyperbolic PDE. The heat exchanged between the pipes of hot and cold fluid induces a coupling between the rightward and leftward equations, which increases the difficulty of solving the PDE system. The estimation objective is addressed by the design of an observer using a PDE approach, which uses boundary measurements to estimate the distributed profiles. The convergence of the observation error is established using Lyapunov analysis. Simulation results illustrate the efficiency of our method using a simulator with time-varying parameters validated on experimental data.

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Section: Simulation Resultsmentioning

confidence: 99%

PDE Observer Design for Counter-Current Heat Flows in a Heat-Exchanger

2017

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“…We aim at using the output y in (6) to identify a stabilizing supervisory control for system (1)- (5).…”

Section: Problem Statementmentioning

confidence: 99%

“…Definition 4 Let consider system (1), (2) along with the boundary condition (10) and the initial conditions (4) and (5). It is said to be Input-to-State-Stable (ISS) in the L 2 -norm with respect to input δ in L 2 (0, ∞) if there exist ν > 0, C > 0, and a K-function θ, such that, for every initial condition u 0 , v 0 ∈ E, the solution satisfies, for all t ≥ 0,…”

Section: Problem Statementmentioning

confidence: 99%

“…Then, let us denote by e i (t), i ∈ I, the measurement deviation with respect to the output of system (1)- (5) e…”

Section: Multi-estimator Structurementioning

confidence: 99%

“…It shows the great potential of industrial applications linked to these models. Thus, a large number of results showed up these last two decades: adaptive observers [2,3], adaptive control [4], stability analysis and controller synthesis based on Linear Matrix Inequalities (LMI) [5], control of switched hyperbolic systems [6,7], etc.…”

Section: Introductionmentioning

confidence: 99%

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Supervisory switching control for linear hyperbolic systems

Lamare

2019

Automatica

Self Cite

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We consider the stabilization problem for linear systems of balance laws subject to uncertain gains affecting the boundary conditions and the reaction term. The stabilization is achieved using the supervisory control, a well established approach in finite dimension. In the context where a controller exists for each estimator, the supervisory control with a performance signal built with the boundary output effectively steers the system to the origin. This novel approach is illustrated with a traffic flow control problem modelled by the Aw-Rascle-Zhang equations.

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Boundary control design for conservation laws in the presence of measurement disturbances

Ferrante

Prieur

2021

Math. Control Signals Syst.

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An optimisation approach for stability analysis and controller synthesis of linear hyperbolic systems

Cited by 14 publications

References 16 publications

PDE Observer Design for Counter-Current Heat Flows in a Heat-Exchanger

PDE Observer Design for Counter-Current Heat Flows in a Heat-Exchanger

Supervisory switching control for linear hyperbolic systems

Boundary control design for conservation laws in the presence of measurement disturbances

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