arXiv subjects

Hannes Gernandt

Publications and source records attributed to Hannes Gernandt.

At least 19 recordsLinked to original sources

arXiv2026

Dissipativity properties of a class of nonlinear time-delay systems via Bessel-Legendre inequalities

Time delays are inherent in many physical and engineered systems and can significantly affect their stability and performance. In this work, we investigate the dissipativity of a class of nonlinear time-delay systems with multiple discrete delays and derive sufficient conditions for both delay-dependent and delay-independent dissipativity using Bessel-Legendre inequalities. For linear systems, the resulting dissipativity conditions are expressed in terms of linear matrix inequalities (LMIs) which can be solved numerically to obtain Lyapunov-Krasovskii-type storage functions.

math.OC↗

arXiv2026

Euler Time-Discretization of Funnel-Controlled Dynamics

We analyze explicit and implicit Euler discretizations of the continuous-time closed-loop dynamics generated by a funnel controller for a fully actuated nonlinear full-state system of relative degree one with scalar positive input gain. A quantitative continuous-time funnel margin provides the compactness and regularity bounds needed for the error analysis. For explicit Euler, a computable upper step-size threshold guarantees a global nodewise distance from the funnel boundary. We show that first-order convergence holds on finite time horizons and, under a~dissipativity condition (a~one-sided Lipschitz bound on the plant dominated by the funnel damping), uniformly in time. For implicit Euler, an admissible update exists for every step size and every trajectory initialized in the funnel retains a step-size-independent nodal margin. Under dissipativity, the admissible root is unique for every step size, the discrete flow is contractive, and the first-order error bound is uniform in time.

math.OC↗

arXiv2026

Block numerical ranges for linear relations

Linear relations are multivalued generalizations of linear operators whose spectral properties are closely linked to the stability of differential-algebraic equations. Consequently, reliable spectral enclosures are of considerable interest. In this note, we extend the established concept of the block numerical range from operators to linear relations by means of a range representation. Unlike the classical numerical range, the resulting block numerical range may be nonconvex and can therefore detect gaps in the spectrum. We establish fundamental properties of this new notion and derive corresponding spectral enclosure results. Finally, we illustrate the theory with a numerical example comparing the block numerical ranges obtained from different constructions. As an application, we obtain an explicit left-half-plane spectral bound for a class of port-Hamiltonian DAEs.

math.SP↗

arXiv2026

Nonlinear port-Hamiltonian system identification from input-state-output data (ISO-pHNN)

In this paper, we introduce a framework called ISO-pHNN for identifying nonlinear port-Hamiltonian systems using input-state-output data. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured way. We explore different architectures based on MLPs, KANs, and using prior information. The identification technique is validated through examples featuring nonlinearities in either the skew-symmetric terms, the dissipative terms, or the Hamiltonian. We show that incorporating a port-Hamiltonian structure does not lower the accuracy and that using additional prior information improves long-term predictions.

eess.SY↗

arXiv2026

On the Numerical Range of Linear Relations in Banach Spaces

This paper is devoted to the study of the numerical range of linear relations in Banach spaces. We present a new definition adapted to the multivalued nature of linear relations and analyze its main properties. We establish spectral inclusion results showing that the spectrum is contained in the union of the closure of the numerical range of a linear relation and the numerical range of its Banach adjoint, together with resolvent estimates related to the distance to the numerical range. As an application, we derive spectral enclosures for operator pencils by associating them with suitable linear relations and introduce corresponding numerical ranges for operator pencils in Banach spaces. We show that this approach may provide sharper information than classical numerical ranges of operator pencils. Furthermore, we use the numerical abscissas to show that the Banach space numerical range can yield strict exponential decay for semigroups that cannot be obtained from the corresponding Hilbert space numerical range.

math.FA↗

arXiv2026

Optimization-based control by interconnection of nonlinear port-Hamiltonian systems

In this paper, we develop a control-by-interconnection approach for the stabilization of nonlinear port-Hamiltonian systems. Motivated by model predictive control, the controller is realized as a continuous-time primal-dual gradient flow associated with a finite-horizon, control-constrained optimal control problem. By exploiting its port-Hamiltonian structure, the optimization dynamics are interconnected with the nonlinear plant. Introducing a time-scale parameter for the optimization dynamics reveals a singularly perturbed closed-loop system, whose reduced dynamics correspond to the optimal finite-horizon feedback, while the boundary-layer dynamics capture convergence of the primal-dual variables to the optimality system. Using a composite Lyapunov function and singular-perturbation arguments, we prove asymptotic stability of the coupled plant-controller dynamics, which is local for sufficiently fast optimization dynamics and becomes global under additional assumptions. Numerical experiments for a nonlinear port-Hamiltonian oscillator illustrate the results.

math.OC↗

arXiv2026

Well-posedness and passivity for a class of bilinear control systems

We study an abstract class of bilinear infinite-dimensional systems that arises in various applications, including district heating systems and quantum control. First, we analyze the existence of mild and classical solutions for abstract bilinear systems with admissible input operators in Banach spaces and study continuous dependence on the data. When the underlying space is a Hilbert space, these results are used to show passivity for a suitably defined co-located output and for mild solutions. The results are applied to the bilinear Schrödinger equation, the Fokker--Planck equation, and a district heating or cooling pipe.

math.AP↗

arXiv2026

Data-driven feedback rectification of switched linear systems

In this paper, a data-driven method for the computation of stabilizing state-feedbacks is proposed that leads to a rectified eigenstructure of switched linear systems. This means that all switching subsystems have the same sets of eigenvectors and the rectification allows to compute a common quadratic Lyapunov function ensuring asymptotic stability of the closed-loop system. The method is illustrated for two examples including a model of an aerosonde.

math.OC↗

arXiv2026

Delay-dependent passivity and stability of linear port-Hamiltonian systems

We study delay-dependent and independent passivity properties of linear port-Hamiltonian systems with delay terms. We derive passivity conditions using a particular storage function and Wirtinger-based inequalities. Furthermore, we recall several conditions for delay-dependent and independent exponential stability. Finally, we present an application of our passivity and stability results to delay equations arising in the modeling of district heating networks and oscillators with delayed damping and stiffness.

math.OC↗

arXiv2026

Coupling optimization algorithms and monotone control systems: Suboptimal model predictive control as an operator splitting scheme

We propose a framework for suboptimal model predictive control (MPC) based on the interconnection of monotone dynamical systems, such as port-Hamiltonian systems. In contrast to classical MPC formulations, where the optimizer is treated as an instantaneous mapping, we model both the plant and the optimizer as dynamical systems and couple them through a structured interconnection. This leads to a continuous-time closed-loop formulation governed by (quasi-)monotone operators. Within this setting, we establish well-posedness of the coupled optimizer-plant dynamics and provide a unified interpretation of suboptimal MPC schemes. In particular, we reveal a direct connection between iterative optimization algorithms and dynamical control systems theory by showing that standard suboptimal MPC algorithms can be understood as time discretizations of the underlying continuous-time dynamics via operator splitting methods.

math.OC↗

arXiv2026

Neural Scaling Laws for Learning-based Identification of Nonlinear Systems

The use of machine learning models in system identification has increased due to their ability to approximate complex nonlinear dynamics with high accuracy. However, often it is not clear how the performance of trained models scales with given resources such as data, compute, and model size. To allow for a better understanding of the scalability of the performance of machine learning models, we verify neural scaling laws (NSLs) in the context of system identification from input-state-output data using different evaluation metrics for accuracy and different system architectures, including input-affine and physics-informed port-Hamiltonian representations. Our verified NSLs can help to forecast performance improvements and guide model design or data acquisition.

math.OC↗

arXiv2026

Stabilization of monotone control systems with input constraints

We present a stabilizing output-feedback controller for nonlinear finite and infinite-dimensional control systems governed by monotone operators that respects given input constraints. In particular, we show under a detectability-like assumption that a saturated version of the classical output feedback controller in passivity-based control achieves control-constrained stabilization as long as the control corresponding to the desired equilibrium is in the interior of the control constraint set. We illustrate our findings using a heat equation, a wave equation, and a finite-dimensional nonlinear port-Hamiltonian system.

math.OC↗

arXiv2025

Long- and short-time behavior of hypocoercive evolution equations with higher index via modal decompositions

Hypocoercivity emerged in kinetic transport theory, allowing to derive exponential long-time estimates for evolution equations. Recently, the short-time asymptotics for equations with dissipative generators were obtained using the hypocoercivity index that is in finite dimensions surprisingly given by a Kalman-type rank condition well-known in control theory. However, the situation for unbounded generators is only understood for index one if modal decompositions are available. Here, we prove long- and short-time estimates for unbounded generators with higher index admitting a modal decomposition. Additionally, an explicit Lyapunov functional is constructed. The result is applied to a class of port-Hamiltonian systems with distributed dissipation.

math.AP↗

arXiv2025

A Port-Hamiltonian Modeling Approach for Integrated Hydrogen Systems

Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct properties, particularly the coupling of hydrogen pipes with electrolyzers, fuel cells, and electrically driven compressors. In this work, we present a unified systematic port-Hamiltonian (pH) framework for modeling hydrogen systems, which inherently provides a passive input-output map of the overall interconnected system and, thus, a promising foundation for structured analysis, control and optimization of this type of newly emerging energy systems.

math.OC↗

arXiv2025

Two energy methods for distributed port-Hamiltonian systems and their application to stability analysis

We develop two local energy methods for distributed parameter port-Hamiltonian (pH) systems on one-dimensional spatial domains. The methods are applied to derive a characterization of exponential stability directly in terms of the energy passing through the boundary over a given time horizon. The resulting condition is verified for a network of vibrating strings where existing sufficient conditions cannot be applied. Moreover, we use a local energy method to study the short-time behavior of pH systems with boundary damping which was recently studied in the context of hypocoercivity.

math.OC↗

arXiv2025

Extension theory via boundary triplets for infinite-dimensional implicit port-Hamiltonian systems

The solution of constrained linear partial-differential equations can be described via parametric representations of linear relations. To study these representations, we provide a novel definition of boundary triplets for linear relations in range representations where the associated boundary map is defined on the domain of the parameterizing operators rather than the relation itself. This allows us to characterize all boundary conditions such that the underlying dynamics is represented by a self-adjoint, skew-adjoint or maximally dissipative relation. The theoretical results are applied to a class of implicit port-Hamiltonian systems on one-dimensional spatial domains. More precisely, we explicitly construct a boundary triplet which solely depends on the coefficient matrices of the involved matrix differential operators and we derive the associated Lagrangian subspace. We exemplify our approach by means of the Dzektser equation, the biharmonic wave equation, and an elastic rod with non-local elasticity condition.

math.AP↗

arXiv2025

Exact Time-Varying Turnpikes for Dynamic Operation of District Heating Networks

District heating networks (DHNs) are crucial for decarbonizing the heating sector. Yet, their efficient and reliable operation requires the coordination of multiple heat producers and the consideration of future demands. Predictive and optimization-based control is commonly used to address this task, but existing results for DHNs do not account for time-varying problem aspects. Since the turnpike phenomenon can serve as a basis for model predictive control design and analysis, this paper examines its role in DHN optimization by analyzing the underlying optimal control problem with time-varying prices and demands. That is, we derive conditions for the existence of a unique time-varying singular arc, which constitutes the time varying turnpike, and we provide its closed-form expression. Additionally, we present converse turnpike results showing a exact time-varying case implies strict dissipativity of the optimal control problem. A numerical example illustrates our findings.

math.OC↗

arXiv2024

Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems

The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying port-Hamiltonian systems are passive, have nonnegative supply rates, and solve (under different smoothness assumptions) Kalman-Yakubovich-Popov differential and integral inequalities. The converse relations are also studied in detail. In particular, sufficient conditions are presented to obtain a port-Hamiltonian representation starting from any of the other dissipativity concepts. Two applications are presented.

math.OC↗