Polynomial Optimization and Optimal Control
Topic: Optimal control | All
Thursday 7th October 2021, 4pm – 5pm.
SPEAKER
Didier Henrion, LAAS-CNRS, University of Toulouse, France and Czech Technical University in Prague, Czechia
ABSTRACT
The moment-sum-of-squares hierarchy allows to solve globally nonconvex optimization problems with polynomial data at the price of solving a family of convex relaxations of increasing size, typically semidefinite programming problems. The propose of the talk is to explain how this approach can be extended to polynomial optimal control, what are the convergence guarantees of the hierarchy in this case, and how optimal trajectories can be approximated from the solutions of the convex relaxations with the help of the Christoffel-Darboux polynomial.
BIO
Didier Henrion was born in 1971 in France. He is a CNRS senior researcher at LAAS, Toulouse, France. He is also a Professor at the Faculty of Electrical Engineering of the Czech Technical University in Prague, Czechia. He is interested in convex optimization, real algebraic geometry, functional analysis and dynamical systems, focusing on the development of constructive tools for addressing mathematical problems arising from systems control. He has been on the editorial boards of the journals Automatica, IEEE Transactions on Automatic Control, Mathematics of Control, Signals and Systems and SIAM Journal on Optimization.
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SPEAKER
Didier Henrion, LAAS-CNRS, University of Toulouse, France and Czech Technical University in Prague, Czechia
ABSTRACT
The moment-sum-of-squares hierarchy allows to solve globally nonconvex optimization problems with polynomial data at the price of solving a family of convex relaxations of increasing size, typically semidefinite programming problems. The propose of the talk is to explain how this approach can be extended to polynomial optimal control, what are the convergence guarantees of the hierarchy in this case, and how optimal trajectories can be approximated from the solutions of the convex relaxations with the help of the Christoffel-Darboux polynomial.
BIO
Didier Henrion was born in 1971 in France. He is a CNRS senior researcher at LAAS, Toulouse, France. He is also a Professor at the Faculty of Electrical Engineering of the Czech Technical University in Prague, Czechia. He is interested in convex optimization, real algebraic geometry, functional analysis and dynamical systems, focusing on the development of constructive tools for addressing mathematical problems arising from systems control. He has been on the editorial boards of the journals Automatica, IEEE Transactions on Automatic Control, Mathematics of Control, Signals and Systems and SIAM Journal on Optimization.
Download Slides