Seminar Details
2013-02-19 (14.00) : An introduction to the moment approach for optimal control
At Euler building
Organized by Mathematical Engineering
Speaker :
Mathieu Claeys
Abstract :
This tutorial talk is devoted to the moment/sum-of-squares approach, which provides a general framework for global optimization of many
problems, including optimal control.
In the first part of the talk, we will review the philosophy of the approach on the problem of global minimization of a polynomial function, for
which the user-friendly GloptiPoly toolbox is readily available. The focus will therefore be on introducing the mathematical tools, such as measure
theory, and the elegant transformations that are used behind the scene by the software: transformation of the original problem into a linear problem
on measures, then manipulation of those measures by their moments to obtain tractable semi-definite relaxations.
The second part of the talk will show how to extend the approach for functional optimization problems such as optimal control. Measures arise quite
naturally in this context, and the moment approach is therefore well suited to tackle those problems fruitfully. This will be shown on the two examples
of bounded and impulsive control problems.