88 citations · 467 across the 63 of their papers we have counts for
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Differentiability of the Value Function on of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems under Control Constraints
Karl Kunisch, Buddhika Priyasad
An abstract framework guaranteeing the continuous differentiability of local value functions on associated with optimal stabilization problems subject to abstract semiline…
Stabilizability for nonautonomous linear parabolic equations with actuators as distributions
Karl Kunisch, Sérgio S. Rodrigues, Daniel Walter
The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as d…
Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems
Karl Kunisch, Gengsheng Wang, Huaiqiang Yu
A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition…
Stabilization of uncertain linear dynamics: an offline-online strategy
Philipp A. Guth, Karl Kunisch, Sérgio S. Rodrigues
A strategy is proposed for adaptive stabilization of linear systems, depending on an uncertain parameter. Offline, the Riccati stabilizing feedback input control operators, corresp…
Ensemble Feedback Stabilization of Linear Systems
Philipp A. Guth, Karl Kunisch, Sergio S. Rodrigues
Stabilization of linear control systems with parameter-dependent system matrices is investigated. A Riccati based feedback mechanism is proposed and analyzed. It is constructed by…
Optimal polynomial feedback laws for finite horizon control problems
Karl Kunisch, Donato Vásquez-Varas
A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality…
Analysis of RHC for stabilization of nonautonomous parabolic equations under uncertainty
Behzad Azmi, Lukas Herrmann, Karl Kunisch
Stabilization of a class of time-varying parabolic equations with uncertain input data using Receding Horizon Control (RHC) is investigated. The diffusion coefficient and the initi…
Global stabilizability to trajectories for the Schlögl equation in a Sobolev norm
Karl Kunisch, Sérgio S. Rodrigues
The stabilizability to trajectories of the Schlögl model is investigated in the norm of the natural state space for strong solutions, which is strictly contained in the standard pi…
Learning Optimal Feedback Operators and their Polynomial Approximation
Karl Kunisch, Donato Vásquez-Varas, Daniel Walter
A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its…
Improving the Convergence Rates for the Kinetic Fokker-Planck Equation by Optimal Control
Tobias Breiten, Karl Kunisch
The long time behavior and detailed convergence analysis of Langevin equations has received increased attention over the last years. Difficulties arise from a lack of coercivity, u…
Shape Derivative for Penalty-Constrained Nonsmooth-Nonconvex Optimization: Cohesive Crack Problem
Victor A. Kovtunenko, Karl Kunisch
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability.…
Infinite Horizon Optimal Control Problems for a Class of Semilinear Parabolic Equations
Eduardo Casas, Karl Kunisch
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in ti…
Optimal Control of Semilinear Parabolic Equations with Non-smooth Pointwise-Integral Control Constraints in Time-Space
Eduardo Casas, Karl Kunisch
This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form for $t \in (0,T…
Saturated feedback stabilizability to trajectories for the Schlögl parabolic equation
Behzad Azmi, Karl Kunisch, Sérgio S. Rodrigues
It is shown that there exist a finite number of indicator functions, which allow us to track an arbitrary given trajectory of the Schlögl model, by means of an explicit saturated f…
On fast convergence rates for generalized conditional gradient methods with backtracking stepsize
Karl Kunisch, Daniel Walter
A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredi…
Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on under Control Constraints
Karl Kunisch, Buddhika Priyasad
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabo…
Design of the monodomain model by artificial neural networks
Sebastien Court, Karl Kunisch
We propose an optimal control approach in order to identify the nonlinearity in the monodomain model, from given data. This data-driven approach gives an answer to the problem of s…
Learning an optimal feedback operator semiglobally stabilizing semilinear parabolic equations
Karl Kunisch, Sérgio S. Rodrigues, Daniel Walter
Stabilizing feedback operators are presented which depend only on the orthogonal projection of the state onto the finite-dimensional control space. A class of monotone feedback ope…
Stabilization of nonautonomous parabolic equations by a single moving actuator
Behzad Azmi, Karl Kunisch, Sérgio S. Rodrigues
It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the sta…
Optimal Control of the 2D Evolutionary Navier-Stokes Equations with Measure Valued Controls
Eduardo Casas, Karl Kunisch
In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier-Stokes system. Looking for sparsity, we take controls as functions of time taking…
Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression
Behzad Azmi, Dante Kalise, Karl Kunisch
A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed. The approach exploits the control…
An inverse problem involving a viscous Eikonal equation with applications in electrophysiology
Karl Kunisch, Philip Trautmann
In this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as an least squa…
Policy iteration for Hamilton-Jacobi-Bellman equations with control constraints
Sudeep Kundu, Karl Kunisch
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analys…
Neural Network Based Nonlinear Observers
Tobias Breiten, Karl Kunisch
Nonlinear observers based on the well-known concept of minimum energy estimation are discussed. The approach relies on an output injection operator determined by a Hamilton-Jacobi-…