Michael Dellnitz
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Multiobjective Optimization of Non-Smooth PDE-Constrained Problems Open
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compu…
On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies Open
In this article we investigate the convergence behavior of gathering protocols with fixed circulant topologies using tools form dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we model a (linear) g…
Efficient Time-Stepping for Numerical Integration Using Reinforcement Learning Open
Many problems in science and engineering require an efficient numerical\napproximation of integrals or solutions to differential equations. For systems\nwith rapidly changing dynamics, an equidistant discretization is often\ninadvisable as…
Efficient time stepping for numerical integration using reinforcement learning Open
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…
Deep model predictive flow control with limited sensor data and online learning Open
The control of complex systems is of critical importance in many branches of science, engineering, and industry, many of which are governed by nonlinear partial differential equations. Controlling an unsteady fluid flow is particularly imp…
ROM-based multiobjective optimization of elliptic PDEs via numerical continuation Open
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to com…
Pareto Explorer: a global/local exploration tool for many-objective optimization problems Open
Multi-objective optimization is an active field of research that has many applications. Owing to its success and because decision-making processes are becoming more and more complex, there is a recent trend for incorporating many objective…
Deep Model Predictive Control with Online Learning for Complex Physical Systems Open
The control of complex systems is of critical importance in many branches of science, engineering, and industry. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g…
Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems Open
Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of th…
View article: A set-oriented path following method for the approximation of parameter dependent attractors
A set-oriented path following method for the approximation of parameter dependent attractors Open
In this work we present a set-oriented path following method for the computation of relative global attractors of parameter-dependent dynamical systems. We start with an initial approximation of the relative global attractor for a fixed pa…
On the hierarchical structure of Pareto critical sets Open
In this talk we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the Pareto…
Improved Neural Control of Movements Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics Open
It is well-established that expertise developed through continuous and deliberate practice has the potential to delay age-related decline in fine motor skills. However, less is known about the underlying mechanisms, that is, whether expert…
A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction Open
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compu…
A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction Open
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compu…
A Survey of Recent Trends in Multiobjective Optimization – Surrogate Models, Feedback Control and Objective Reduction Open
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compu…
Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives Open
Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.e. accuracy) and computational burden has to be made. This …
A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems Open
In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained probl…
POD‐based multiobjective optimal control of PDEs with non‐smooth objectives Open
A framework for set‐oriented multiobjective optimal control of partial differential equations using reduced order modeling has recently been developed [1]. Following concepts from localized reduced bases methods, error estimators for the r…
Transition Manifolds of Complex Metastable Systems Open
We consider complex dynamical systems showing metastable behavior but no\nlocal separation of fast and slow time scales. The article raises the question\nof whether such systems exhibit a low-dimensional manifold supporting its\neffective …
Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics Open
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dyn…
Self-adjoint Matrices are Equivariant Open
In this short note we prove that a matrix $A\in\mathbb{R}^{n,n}$ is self-adjoint if and only if it is equivariant with respect to the action of a group $Γ\subset {\bf O}(n)$ which is isomorphic to $\otimes_{k=1}^n\mathbf{Z}_2$. Moreover we…
A Comparison of two Predictive Approaches to Control the Longitudinal Dynamics of Electric Vehicles Open
In this contribution we compare two different approaches to the implementation of a Model Predictive Controller in an electric vehicle with respect to the quality of the solution and real-time applicability. The goal is to develop an intel…
Multiobjective Model Predictive Control of an Industrial Laundry Open
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