Can I read Infinite-Dimensional Sums-of-Squares for Optimal Control on EtoBox?

Infinite-Dimensional Sums-of-Squares for Optimal Control by Berthier, Eloïse; Carpentier, Justin; Rudi, Alessandro; Bach, Francis is a scholarly article available to read on EtoBox.

What is Infinite-Dimensional Sums-of-Squares for Optimal Control about?

We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial optimization to the generic case of smooth problems. Such a representation is infinite-dimensional and relies on a particular space of functions-a reproducing kernel Hilbert space-chosen to fit the structure of the control problem. After subsampling, it leads to a practical method that amounts to solving a semi-definite program. We illustrate our approach by a numerical application on a simple low-dimensional control problem.

Author

Berthier, Eloïse; Carpentier, Justin; Rudi, Alessandro; Bach, Francis

Published

2021

Language

EN