Stabilization of a System of &lt;formula formulatype="inline"&gt; &lt;tex Notation="TeX"&gt;$n+1$&lt;/tex&gt;&lt;/formula&gt; Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input

Meglio, Florent Di; Vázquez, Rafael; Krstić, Miroslav

doi:10.1109/tac.2013.2274723

Cited by 263 publications

(169 citation statements)

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“…In this work one boundary condition is supposed to be algebraically related to the other, which allows the authors to build an observer using the measurements from one end of the domain only. Similar ideas are used by Di Meglio et al (2013) to develop a boundary controller-observer for a system of n-rightward and one leftward convecting transport PDE. Castillo et al (2013) designed a boundary observer for a set of rightward quasi-linear hyperbolic transport equations of conservation laws, using the strict Lyapunov method developed by Coron et al (2007).…”

Section: Introductionmentioning

confidence: 97%

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: Introductionmentioning

confidence: 97%

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

2017

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“…Recently, outputfeedback adaptive designs for parabolic PDEs have been developed in Krstic and Smyshlyaev [2008], Smyshlyaev and Krstic [2007a,b], Bekiaris-Liberis et al [2013], BreschPietri et al [2012]. Similarly, in this paper, we extend the backstepping observer of Di Meglio et al [2013a]. This output-feedback design is particularly relevant to the problem of UnderBalanced Drilling.…”

Section: Introductionmentioning

confidence: 93%

“…We introduce a parameter estimateθ(t) and, following Di Meglio et al [2013a], define distributed estimatesû i andv by the following observer equations…”

Section: Adaptive Observer Equationsmentioning

confidence: 99%

“…The uncertainty on the downhole conditions yields uncertain boundary parameters in the linearized model. To address this difficulty, we extend the backstepping transformation introduced in Di Meglio et al [2013a] by considering an adaptation law based on the Gradient Descent technique. We prove exponential convergence of both the parameter estimate and the distributed state, in L 2 -norm.…”

Section: Introductionmentioning

confidence: 99%

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An adaptive observer for hyperbolic systems with application to UnderBalanced Drilling

Meglio

Bresch‐Pietri

Aarsnes

2014

IFAC Proceedings Volumes

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We present an adaptive observer design for a first-order hyperbolic system of Partial Differential Equations with uncertain boundary parameters. The design relies on boundary measurements only, and is based on a backstepping approach. Using a Gradient Descent technique, we prove exponential convergence of the distributed system and estimation of the parameter. This method is applied to the estimation of uncertain parameters during the process of oil well drilling.

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“…A result from [1] gives a necessary and sufficient condition for the existence of a quadratic Lyapunov function. In [9], an example with a stabilising static output feedback has been designed such that the previous condition is violated and thus that there does not exist a quadratic Lyapunov function for this system.…”

Section: λN(x)mentioning

confidence: 99%