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From Open to Closed Loop Optimal Control of PDEs

Total Cost €


EC-Contrib. €






Project "OCLOC" data sheet

The following table provides information about the project.


Organization address
city: GRAZ
postcode: 8010

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Austria [AT]
 Project website
 Total cost 1˙678˙325 €
 EC max contribution 1˙678˙325 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-01-01   to  2021-12-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAET GRAZ AT (GRAZ) coordinator 1˙540˙726.00


 Project objective

The proposal addresses some of the most pressing topics in optimal control of partial differential equations (PDEs): Non-smooth, non-convex optimal control and computational techniques for feedback control. These two topics will be applied to the large scale optimal control problems for the bidomain equations, which are the established model to describe the electrical activity of the heart. Due to their rich dynamical systems behavior these systems are particularly challenging.

The use of non-smooth functionals is of great practical relevance in many diverse situations. They promote sparsity, and provide a perfect formulation for switching and multi-bang controls, and for the optimal actuator location problem. For inverse problems the case $L^{p}$ with $pin (0,1)$ is of special statistical importance, and $L^0$ can be the basis of a new formulation for topology optimization problems. But lack of Lipschitz continuity and of convexity are significant obstacles which can only be overcome by the development of new analytical and numerical concepts. The new algorithmic concepts will also be applicable to important non-smooth problems in continuum mechanics, as for instance the quasi-static evolution of fractures.

Closed loop control is of paramount importance due to its {bf robustness} against system perturbations. Nevertheless, numerical realization of optimal feedback strategies for nonlinear PDEs has barely been touched since the curse of dimensionality makes direct numerical treatment of the Hamilton-Jacobi-Bellman equation unfeasible. We shall therefore develop and analyze suboptimal strategies based on model reduction and interpolation techniques, and on model-predictive control. The availability of boundary and near-to-the boundary measurements together with dynamic observer techniques will allow to test the proposed methods to obtain suboptimal feedback controls for the bidomain equations.


year authors and title journal last update
List of publications.
2018 Victor A. Kovtunenko, Karl Kunisch
Revisiting generalized FEM: a Petrov–Galerkin enrichment based FEM interpolation for Helmholtz problem
published pages: , ISSN: 0008-0624, DOI: 10.1007/s10092-018-0280-5
Calcolo 55/3 2019-07-02
2018 Gilbert Peralta, Karl Kunisch
Interface stabilization of a parabolic-hyperbolic pde system with delay in the interaction
published pages: 3143-3171, ISSN: 1553-5231, DOI: 10.3934/dcds.2018133
Discrete & Continuous Dynamical Systems - A 38/6 2019-07-02
2018 Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Infinite-Horizon Bilinear Optimal Control Problems: Sensitivity Analysis and Polynomial Feedback Laws
published pages: 3184-3214, ISSN: 0363-0129, DOI: 10.1137/18m1173952
SIAM Journal on Control and Optimization 56/5 2019-03-29
2018 Gernot Holler, Karl Kunisch, Richard C Barnard
A bilevel approach for parameter learning in inverse problems
published pages: 115012, ISSN: 0266-5611, DOI: 10.1088/1361-6420/aade77
Inverse Problems 34/11 2019-03-29
2018 Gilbert Peralta, Karl Kunisch
Analysis and finite element discretization for optimal control of a linear fluid–structure interaction problem with delay
published pages: , ISSN: 0272-4979, DOI: 10.1093/imanum/dry070
IMA Journal of Numerical Analysis 2019-03-29
2018 Dante Kalise, Karl Kunisch, Kevin Sturm
Optimal actuator design based on shape calculus
published pages: 2667-2717, ISSN: 0218-2025, DOI: 10.1142/s0218202518500586
Mathematical Models and Methods in Applied Sciences 28/13 2019-03-29
2019 Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Taylor expansions of the value function associated with a bilinear optimal control problem
published pages: , ISSN: 0294-1449, DOI: 10.1016/j.anihpc.2019.01.001
Annales de l\'Institut Henri Poincaré C, Analyse non linéaire 2019-03-29
2019 Daria Ghilli, Karl Kunisch
On monotone and primal-dual active set schemes for $$ell ^p$$ ℓ p -type problems, $$p in (0,1]$$ p ∈ ( 0 , 1 ]
published pages: 45-85, ISSN: 0926-6003, DOI: 10.1007/s10589-018-0036-9
Computational Optimization and Applications 72/1 2019-03-29
2018 Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Numerical study of polynomial feedback laws for a bilinear control problem
published pages: 557-582, ISSN: 2156-8499, DOI: 10.3934/mcrf.2018023
Mathematical Control & Related Fields 8/3 2019-03-29

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