2021/10/14 by Berthier, Eloïse, Carpentier, Justin, Rudi, Alessandro +1 · 1 citation
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2110.07396
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.