Optimal design of sensors and actuators by E. Zuazua

Date: Tue. June 14, 2022
Organized by: CIRM, Centre International de Rencontres Mathématiques (Marseille, France)
Title: Optimal design of sensors and actuators

Speaker: Our Head Prof. Enrique Zuazua
Affiliation: Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Our Head Enrique Zuazua talked about “Optimal design of sensors and actuators” at the Theoretical and Numerical Trends in Inverse Problems and Control for PDEs, and Hamilton-Jacobi Equation: a French-Italian-Japanese Conference, organized from June 13rd to 17th at CIRM-Luminy, Marseille (France) in honor of Piermarco Cannarsa’s 65th. birthday.

Abstract. In this lecture we shall present some recent results in collaboration with B. Geshkovski (MIT) on the design of optimal sensors and actuators for control systems. We shall mainly focus in the finite-dimensional case, using the Brunovsky normal form. This allows to reformulate the problem in a purely matricial context, which permits rewriting the problem as a minimization problem of the norm of the inverse of a change of basis matrix, and allows us to stipulate the existence of minimizers, as well as non-uniqueness, due to an invariance of the cost with respect to orthogonal transformations. We will present several numerical experiments to both visualize these artifacts and also point out towards further directions and open problems, in particular in the context of PDE infinite-dimensional models.


(Courtesy by CIRM)
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This meeting aims to highlight the latest achievements of leading researchers from the French, Italian and Japanese mathematical communities in the Hamilton-Jacobi equation, inverse problems and control theory, as well as younger researchers in the field, in order to discuss and disseminate the latest results and envisage new challenges. Its main purpose is to give an overview of the different aspects of these problems and the various tools employed for solving them, from both theoretical and numerical viewpoints. organized by CIRM.

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