ACIPDif22: Optimal controller design via Brunovsky’s normal form by E. Zuazua

On July 19th, 2022 our Head Prof. Enrique Zuazua will talk on “Optimal controller design via Brunovsky’s normal form” at the ACIPDif22 school-workshop “Analysis, Control & Inverse Problems for Diffusive Systems with Application to Natural and Social Sciences” organized by the Department of Mathematics at University of Bari Aldo Moro (Università degli Studi di Bari Aldo Moro) in hybrid mode (online/in person) in Bari, Italy.

Abstract. By using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the controller which minimizes the controllability cost for finite dimensional linear systems with scalar controls. This reformulation provides a novel perspective to the optimal design problem in the sense that it does not require the matrix generating the dynamics to be diagonalizable, and does not entail a randomization procedure (as done in past literature in diffusion equations and waves).

The resulting optimization problem reduces to a minimization 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 provide illustrations generated by numerical experiments to both visualize these artifacts and also stipulate further directions and open problems.

This is a joint work with Borjan Geshkovski, MIT.

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