Prof. Dr. Falk Hante
Profil
Forschungsthemen2
EXC 2046/1: Math+ Decision-making for Energy Network Dynamics, Teilprojekt: AA4-7
Quelle ↗Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 06/2021 - 05/2024 Projektleitung: Prof. Dr. Falk Hante
SFB/TRR 154/3: Gemischt ganzzahlig-kontinuierliche dynamische Systeme mit partiellen Differentialgleichungen (TP A03)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2022 - 06/2026 Projektleitung: Prof. Dr. Falk Hante
Mögliche Industrie-Partner10
Stand: 26.4.2026, 19:48:44 (Top-K=20, Min-Cosine=0.4)
- 16 Treffer59.4%
- Systematic Models for Biological Systems Engineering Training NetworkP59.4%
- Systematic Models for Biological Systems Engineering Training Network
Protatuans-Etaireia Ereynas Viotechologias Monoprosopi Etaireia Periorisments Eythinis
PT15 Treffer59.4%- Systematic Models for Biological Systems Engineering Training NetworkP59.4%
- Systematic Models for Biological Systems Engineering Training Network
- 16 Treffer59.4%
- Systematic Models for Biological Systems Engineering Training NetworkP59.4%
- Systematic Models for Biological Systems Engineering Training Network
- 16 Treffer59.4%
- Systematic Models for Biological Systems Engineering Training NetworkP59.4%
- Systematic Models for Biological Systems Engineering Training Network
- 3 Treffer59.1%
- Digitalising Mobility and International Networks With Open Education (DIONE)P59.1%
- Digitalising Mobility and International Networks With Open Education (DIONE)
- DYnamic control in hybrid plasmonic NAnopores: road to next generation multiplexed single MOlecule detectionP57.0%
- DYnamic control in hybrid plasmonic NAnopores: road to next generation multiplexed single MOlecule detection
- 2 Treffer55.6%
- Zuwendung im Rahmen des Programms „exist – Existenzgründungen aus der Wissenschaft“ aus dem Bundeshaushalt, Einzelplan 09, Kapitel 02, Titel 68607, Haushaltsjahr 2026, sowie aus Mitteln des Europäischen Strukturfonds (hier Euro-päischer Sozialfonds Plus – ESF Plus) Förderperiode 2021-2027 – Kofinanzierung für das Vorhaben: „exist Women“T55.6%
- Zuwendung im Rahmen des Programms „exist – Existenzgründungen aus der Wissenschaft“ aus dem Bundeshaushalt, Einzelplan 09, Kapitel 02, Titel 68607, Haushaltsjahr 2026, sowie aus Mitteln des Europäischen Strukturfonds (hier Euro-päischer Sozialfonds Plus – ESF Plus) Förderperiode 2021-2027 – Kofinanzierung für das Vorhaben: „exist Women“
- 29 Treffer53.9%
- Integrated Self-Assembled SWITCHable Systems and Materials: Towards Responsive Organic Electronics – A Multi-Site Innovative Training Action (iSwitch)P53.9%
- EU: Bottom-Up Generation of atomicalLy Precise syntheTIc 2D MATerials for High Performance in Energy and Electronic Applications – A Multi-Site Innovative Training Action (ULTIMATE)P50.3%
- Integrated Self-Assembled SWITCHable Systems and Materials: Towards Responsive Organic Electronics – A Multi-Site Innovative Training Action (iSwitch)
- 15 Treffer53.9%
- Integrated Self-Assembled SWITCHable Systems and Materials: Towards Responsive Organic Electronics – A Multi-Site Innovative Training Action (iSwitch)P53.9%
- Integrated Self-Assembled SWITCHable Systems and Materials: Towards Responsive Organic Electronics – A Multi-Site Innovative Training Action (iSwitch)
- 15 Treffer53.9%
- Integrated Self-Assembled SWITCHable Systems and Materials: Towards Responsive Organic Electronics – A Multi-Site Innovative Training Action (iSwitch)P53.9%
- Integrated Self-Assembled SWITCHable Systems and Materials: Towards Responsive Organic Electronics – A Multi-Site Innovative Training Action (iSwitch)
Publikationen25
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Applied Mathematics & Optimization · 68 Zitationen · DOI
Industrial and applied mathematics · 58 Zitationen · DOI
IEEE Transactions on Automatic Control · 52 Zitationen · DOI
We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching. We also provide an explicit dwell-time bound for guaranteeing exponential stability of the switching system when, for each mode, the system is exponentially stable. Our stability conditions only depend on the system parameters and boundary data. These conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption. We present tutorial examples to illustrate the instabilities that can result from switching.
49 Zitationen
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments.
SIAM Journal on Control and Optimization · 45 Zitationen · DOI
We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.
Networks and Heterogeneous Media · 40 Zitationen · DOI
Pipeline networks for gas transportation often contain circles. For such networks it is more difficult to determine the stationary states than for networks without circles. We present a method that allows to compute the stationary states for subsonic pipe flow governed by the isothermal Euler equations for certain pipeline networks that contain circles. We also show that suitably chosen boundary data determine the stationary states uniquely. The construction is based upon novel explicit representations of the stationary states on single pipes for the cases with zero slope and with nonzero slope. In the case with zero slope, the state can be represented using the Lambert--W function.
Lecture notes in computer science · 38 Zitationen · DOI
Nonlinear Analysis Hybrid Systems · 23 Zitationen · DOI
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition times and Lagrange-type cost functions including switching costs. In particular, for a fixed sequence of modes, we derive necessary optimality conditions using an adjoint equation based representation for the gradient of the costs with respect to the switching times. For optimization with respect to the mode sequence, we discuss a mode-insertion gradient. The theory unifies and generalizes similar approaches for evolutions governed by ordinary and delay differential equations. More importantly, it also applies to systems governed by semilinear partial differential equations including switching the principle part. Examples from each of these system classes are discussed.
Journal of Systems Science and Complexity · 14 Zitationen · DOI
Journal of Differential Equations · 13 Zitationen · DOI
Lecture notes in computer science · 11 Zitationen · DOI
arXiv (Cornell University) · 10 Zitationen · DOI
We consider mixed-integer optimal control problems with combinatorial\nconstraints that couple over time such as minimum dwell times. We analyze a\nlifting and decomposition approach into a mixed-integer optimal control problem\nwithout combinatorial constraints and a mixed-integer problem for the\ncombinatorial constraints in the control space. Both problems can be solved\nvery efficiently with existing methods such as outer convexification with\nsum-up-rounding strategies and mixed-integer linear programming techniques. The\ncoupling is handled using a penalty-approach. We provide an exactness result\nfor the penalty which yields a solution approach that convergences to partial\nminima. We compare the quality of these dedicated points with those of other\nheuristics amongst an academic example and also for the optimization of\nelectric transmission lines with switching of the network topology for flow\nreallocation in order to satisfy demands.\n
Industrial and applied mathematics · 9 Zitationen · DOI
Networks and Heterogeneous Media · 9 Zitationen · DOI
We consider model adaptivity for gas flow in pipeline networks. For each instant in time and for each pipe in the network a model for the gas flow is to be selected from a hierarchy of models in order to maximize a performance index that balances model accuracy and computational cost for a simulation of the entire network. This combinatorial problem involving partial differential equations is posed as an optimal switching control problem for abstract semilinear evolutions. We provide a theoretical and numerical framework for solving this problem using a two stage gradient descent approach based on switching time and mode insertion gradients. A numerical study demonstrates the practicability of the approach.
Mathematics of Control Signals and Systems · 8 Zitationen · DOI
Encyclopedia of Optimization · 7 Zitationen · DOI
SIAM Journal on Numerical Analysis · 7 Zitationen · DOI
We prove existence and uniqueness of solutions of an optimization problem with time-periodic parabolic partial differential equation constraints and show that the solution inherits high smoothness properties from the given data. We use the theory of semigroups in conjunction with spectral decompositions of their generators in order to derive detailed representation formulas for shooting operators in function space and their adjoints. A spectral truncation approach delivers a self-adjoint indefinite Newton--Picard preconditioner for the saddle-point system of optimality conditions in function space. We show that this preconditioner leads to convergence in a function space fixed-point iteration. Moreover, we discuss that this preconditioner can be approximated well by a two-grid approach. We address some implementation issues and present numerical results for three-dimensional instationary problems with more than 100,000,000 degrees of freedom.
Stability analysis of linear hyperbolic systems with switching parameters and boundary conditions
20086 Zitationen · DOI
We study asymptotic stability of an infinite dimensional system that switches between a finite set of modes. Each mode is governed by a system of one-dimensional, linear, hyperbolic partial differential equations on a bounded space interval. The switching system is fairly general in that the space dependent system matrix functions as well as the boundary conditions may switch in time. For the case in which the switching occurs between subsystems in canonical diagonal form, we provide two sets of sufficient conditions for asymptotic stability under arbitrary switching signals. These results are direct generalizations of the corresponding results for the unswitched case. Furthermore, we provide an explicit dwell-time bound on the switching signals that guarantee asymptotic stability of the switched system under the assumption that each of the subsystems are stable. Our results of stability under arbitrary switching generalize to the case where switching occurs between non-diagonal hyperbolic systems that are diagonalizable using a common transformation. For the case where no such transformation exists, we prove existence of a dwell-time bound on the switching signals such that asymptotic stability is guaranteed. To motivate our study, we discuss a potential application to stability of water flow in one-dimensional open channels governed by linearized Saint-Venant equations.
at - Automatisierungstechnik · 5 Zitationen · DOI
Abstract This contribution focuses on the analysis and control of friction-dominated flow of gas in pipes. The pressure in the gas flow is governed by a partial differential equation that is a doubly nonlinear parabolic equation of p -Laplace type, where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> <m:mo>=</m:mo> <m:mstyle> <m:mfrac> <m:mrow> <m:mn>3</m:mn> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:mfrac> </m:mstyle> </m:math> p=\frac{3}{2} . Such equations exhibit positive solutions, finite speed of propagation and satisfy a maximum principle. The pressure is fixed on one end (upstream), and the flow is specified on the other end (downstream). These boundary conditions determine a unique steady equilibrium flow. We present a boundary feedback flow control scheme, that ensures local exponential stability of the equilibrium in an <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>L</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> {L^{2}} -sense. The analysis is done both for the PDE system and an ODE system that is obtained by a suitable spatial semi-discretization. The proofs are based upon suitably chosen Lyapunov functions.
5 Zitationen · DOI
We provide necessary and sufficient conditions in terms of the existence of common Lyapunov functions for switched systems with modes governed by strongly continuous semigroups on Banach spaces to be globally uniformly exponentially stable for arbitrary switching signals.
Applied Mathematics & Optimization · 4 Zitationen · DOI
Abstract We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the resulting subproblems as suitably chosen mixed-integer optimal control problems on subintervals in time. An iterative procedure then ensures continuity of the states at the boundaries of the subintervals via co-state information encoded in virtual controls. We prove convergence of this iterative scheme for discrete-continuous linear-quadratic problems and present numerical results both for linear-quadratic as well as nonlinear problems.
3 Zitationen
We consider a direct approach to solve mixed-integer nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach in the sense of the corresponding optimal values. The results are obtained by considering the discretized problem as a parametric mixed-integer nonlinear optimization problem in finite dimensions, where the maximum step size for discretizing the dynamics is the parameter. In this setting, we prove the continuity of the optimal value function under a stability assumption for the integer feasible set and second-order conditions from nonlinear optimization. We address the necessity of the conditions on the example of pipe sizing problems for gas networks.
arXiv (Cornell University) · 3 Zitationen · DOI
Selected results for the stability and optimal control of abstract switched systems in Banach and Hilbert space are reviewed. The dynamics are typically given in a piecewise sense by a family of nonlinearly perturbed evolutions of strongly continuous semigroups. Stability refers to characterizations of asymptotic decay of solutions that holds uniformly for certain classes of switching signals for time going to infinity. Optimal control refers to the minimization of costs associated to solutions by appropriately selecting switching signals. Selected numerical results verify and visualize some of the available theory.
arXiv (Cornell University) · 3 Zitationen · DOI
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition times and Lagrange-type cost functions including switching costs. In particular, for a fixed sequence of modes, we derive necessary optimality conditions using an adjoint equation based representation for the gradient of the costs with respect to the switching times. For optimization with respect to the mode sequence, we discuss a mode-insertion gradient. The theory unifies and generalizes similar approaches for evolutions governed by ordinary and delay differential equations. More importantly, it also applies to systems governed by semilinear partial differential equations including switching the principle part. Examples from each of these system classes are discussed.
OPUS FAU (Kooperativer Bibliotheksverbund Berlin-Brandenburg (KOBV), on behalf of the Universitätsbibliothek Erlangen-Nürnberg) · 3 Zitationen
Hybrid dynamical systems are considered as a design paradigm or multiscale model for networked transport problems. Evolution in time is governed by switching among a family of solutions to vector-valued, semi-linear hyperbolic partial differential equations on a bounded interval in space with reflecting boundary conditions. Existence of generalized solutions and appropriate continuous dependency properties are studied on the discrete-continuous level. In particular, it is shown how the Zeno phenomenon can be avoided, despite the propagation of discontinuities along characteristics resulting from instantanously changing boundary conditions and their interaction with switching rules evaluating pointwise boundary obervation. Moreover, for a given cost function including switching costs, the problem of optimal switching is studied. For scalar equations with boundary switching control, optimality is characterized in terms of a first order necessary condition based on a formula for switching time sensitivity. The results are validated numerically on examples.
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Stammdaten
Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Prof. Dr. Falk Hante
- Titel
- Prof. Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Mathematik
- Arbeitsgruppe
- Angewandte Mathematik mit Schwerpunkt Optimierung komplexer Systeme
- Telefon
- +49 30 2093-45383
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- 26.4.2026, 01:05:49