Exploiting port-Hamiltonian and dissipative structures in numerical optimal control of PDEs

Abstract: In this talk, we explore several ways to leverage (port-)Hamiltonian structures in the solution of optimal control problems.

We first present a novel time-domain decomposition strategy. Therein, the optimality system is formulated as a sum of dissipative operators, which enables a Peaceman–Rachford and Dougla-Rachford-type fixed-point iterations in function space. The resulting subproblems correspond to local optimal control problems on shorter time horizons and can be solved in parallel. Using the dissipativity of the formulation, we establish convergence of the method.

In the second part, we focus on tailored iterative solvers for linear systems arising from the discretization of port-Hamiltonian optimal control problems. In particular, we will inspect Krylov subspace methods that utilize the symmetric part of the operator as a preconditioner to guarantee mesh-independent convergence.

We illustrate our results by means of various large-scale problems from fluid mechanics, elasticity or advection-diffusion phenomena.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

Port-Hamiltonian Seminar

Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY