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Boundary Control for Stabilization of Large-Scale Networks through the Continuation Method

Denis Nikitin 1 Carlos Canudas de Wit 1 Paolo Frasca 1 
1 DANCE - Dynamics and Control of Networks
Inria Grenoble - Rhône-Alpes, GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
Abstract : In this work we study a continuation method which transforms spatially distributed ODE systems into PDEs that respect the spatial structure of the original ODE systems. Such PDE description can be used not only for analysis but also for a continuous control design which, being discretized back, results in a nontrivial control law for the original ODE system. In this paper we focus on the continuation for linear systems, including multidimensional inhomogeneous systems and in particular linear networks, showing that such systems can be transformed into general second-order parabolic PDEs. The method is applied to the stabilization of a chain of coupled semiconductor lasers. We obtain a PDE model of this system, design a backstepping-based boundary control to stabilize the obtained PDE and then translate the control policy back to the original laser chain, effectively stabilizing it.
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https://hal.archives-ouvertes.fr/hal-03211021
Contributor : Denis Nikitin Connect in order to contact the contributor
Submitted on : Wednesday, April 28, 2021 - 1:13:30 PM
Last modification on : Sunday, June 26, 2022 - 3:07:44 AM
Long-term archiving on: : Thursday, July 29, 2021 - 6:41:12 PM

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  • HAL Id : hal-03211021, version 1

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Denis Nikitin, Carlos Canudas de Wit, Paolo Frasca. Boundary Control for Stabilization of Large-Scale Networks through the Continuation Method. CDC 2021 - 60th IEEE Conference on Decision and Control, Dec 2021, Austin, Texas, United States. pp.4786-4791. ⟨hal-03211021⟩

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