Christophe Prieur

RL4, Publisher: SIAM J. Control Optim., Link>


Christophe Prieur, Constantinos Kitsos, Eduardo Cerpa, Gildas Besancon


This paper is about the stabilization of a cascade system of $n$ linear Korteweg--de Vries equations in a bounded interval. It considers an output feedback control placed at the left endpoint of the last equation, while the output involves only the solution to the first equation. The boundary control problems investigated include two cases: a classical control on the Dirichlet boundary condition and a less standard one on its second-order derivative. The feedback control law utilizes the estimated solutions of a high-gain observer system, and the output feedback control leads to stabilization for any $n$ for the first boundary conditions case and for $n=2$ for the second one.

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RL4, Publisher: Mathematical Control and Related Fields, Link>


Christophe Prieur, Eduardo Cerpa, Esteban Hernández


In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume the existence of an appropriate estimator, which has been established in the literature using voltage measurements. By applying backstepping and Lyapunov tools, we are able to build observers and to design output feedback controllers giving a positive answer to the SOC tracking problem. We provide convergence proofs and perform some numerical simulations to illustrate our theoretical results.

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