arXiv subjects

Henk J. van Waarde

Publications and source records attributed to Henk J. van Waarde.

At least 19 recordsLinked to original sources

arXiv2026

Data-Driven Stabilization Using Prior Knowledge on Stabilizability and Controllability

In this work, we study data-driven stabilization of linear time-invariant systems using prior knowledge of system-theoretic properties, specifically stabilizability and controllability. To formalize this, we extend the concept of data informativity by requiring the existence of a controller that stabilizes all systems consistent with the data and the prior knowledge. We show that if the system is controllable, then incorporating this as prior knowledge does not relax the conditions required for data-driven stabilization. Remarkably, however, we show that if the system is stabilizable, then using this as prior knowledge leads to necessary and sufficient conditions that are weaker than those for data-driven stabilization without prior knowledge. In other words, data-driven stabilization is easier if one knows that the underlying system is stabilizable. We also provide new data-driven control design methods in terms of linear matrix inequalities that complement the conditions for informativity.

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arXiv2026

Bridging Model Reference Adaptive Control and Data Informativity

The goal of model reference adaptive control (MRAC) is to ensure that the trajectories of an unknown dynamical system track those of a given reference model. This is done by means of a feedback controller that adaptively changes its gains using data collected online from the closed-loop system. One of the approaches to solve the MRAC problem is to impose conditions on the data that guarantee convergence of the gains to a solution of the so-called matching equations. In the literature, various extensions of the concept of persistent excitation have been proposed in an effort to weaken the conditions on the data required for this convergence. Despite these efforts, it is not well-understood what conditions are necessary and sufficient for ensuring convergence of MRAC to a solution of the matching equations. In this paper, we propose a new framework to study the MRAC problem, using the concept of data informativity. Our main contribution is to provide \emph{necessary and sufficient} conditions for the existence of an adaptive law that guarantees convergence of the gains to a solution of the matching equations, and to provide a recipe for its construction. While existing excitation conditions imply that the system can be uniquely identified from the collected data, our results show that this is not necessary for the convergence of the feedback gains.

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arXiv2026

A Generalized Stability Theorem for Interconnections of Dissipative Behaviors

Dissipativity theory enables the stability analysis of complex, interconnected systems through the physical properties of their components. Celebrated examples of such stability results include the small gain and passivity theorems. In this paper, we prove a unifying stability theorem for dissipative linear time-invariant (LTI) systems. We use the behavioral approach to express storage functions and supply rates in terms of quadratic differential forms (QDFs). Our main result establishes conditions for the stability of an interconnection of two LTI behaviors that are both dissipative with respect to general, dynamic supply rates. As special cases, we recover existing results for static supply rates, such as those capturing finite $L_2$-gain and passivity, as well as dynamic ones capturing, for example, delta dissipativity. The key idea of the paper is to construct a Lyapunov function as a sum of storage functions and a coupling QDF, thereby allowing for a richer class of Lyapunov functions than existing works dealing with just sums of storage functions.

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arXiv2026

Robust stabilization of discrete-time linear systems requires nonlinear dynamic feedback

This paper studies the problem of robust stabilization of linear input-state systems in discrete time. We prove that for any compact set of stabilizable systems, there exists a dynamic state-feedback controller that globally asymptotically stabilizes all systems in the set. In addition, we show that for some compact sets of stabilizable systems, no nonlinear static or linear dynamic state-feedback law can achieve this task. This proves that, in general, robust stabilization requires a feedback law that is both nonlinear and dynamic. We extend our study to robust exponential stabilization with a given rate of decay. Finally, for polytopic sets of systems, we introduce an algorithm for the design of robust feedback laws.

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arXiv2026

Online experiment design for continuous-time systems using generalized filtering

The goal of experiment design is to select the inputs of a dynamical system in such a way that the resulting data contain sufficient information for system identification and data-driven control. This paper investigates the problem of experiment design for continuous-time systems under piecewise constant input signals. To obviate the need for measuring time derivatives of (data) trajectories, we introduce a generalized filtering framework. Our main result is to establish conditions on the input and the filter functions under which the filtered data are informative for system identification, i.e., they satisfy a certain rank condition. We assume that the filter functions are piecewise continuously differentiable, encompassing several filter functions that have appeared in the literature. Building on the proposed filtering framework, we develop an experiment design procedure, adapted from experiment design results for discrete-time systems, where the piecewise constant input signal is designed online during system operation. This method is shown to be sample efficient, in the sense that it deals with the least possible number of filtered data samples for system identification. Notably, the designed input signal is such that the data capture the system's dynamics at all times between sampling instants, thus establishing a connection with a continuous-time version of Willems et al.'s fundamental lemma.

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arXiv2026

Experiment Design for Set-membership Identification: From Prior Knowledge to Universal Inputs

We consider the problem of designing input signals for an unknown linear time-invariant system in such a way that the resulting data, within a finite horizon, is suitable for identification with a desired accuracy. We consider both noise-free and noisy settings with $\ell_\infty$--bounded noise models. We will take into account general prior knowledge of the system parameters. Central in our study is the concept of universal inputs. An input is called universal for identification if, when applied to any system complying with the prior knowledge, it yields data suitable for accurate identification. We provide new methods for designing such universal inputs. Our results generalize the experiment design approach based on Willems et al.'s fundamental lemma that relies on persistently exciting inputs, and that is limited to prior knowledge on controllability. It turns out that for other types of prior knowledge, there exist universal inputs that outperform the persistently exciting ones, e.g., in terms of sample efficiency. Moreover, we investigate types of prior knowledge that enable experiment design for exact identification in the presence of noise.

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arXiv2026

A New Noise Model for Data-driven Control: Generalized Frobenius Norm Bounds

In this article, we introduce a new noise model for data-driven control. The model can be interpreted as a generalization of a Frobenius norm bound on the matrix of noise samples. For instantaneously bounded noise, the proposed model provides a less conservative overapproximation than an existing noise model based on a quadratic matrix inequality (QMI). Using the new model, we derive necessary and sufficient conditions for data-driven control. The framework covers a broad class of design problems, including quadratic stabilization, $\mathcal{H}_2$ control and $\mathcal{H}_{\infty}$ control, and is further extended to cover data-driven analysis problems, ranging for stabilizability to dissipativity. A key technical contribution is a new type of S-lemma that offers necessary and sufficient conditions under which a quadratic matrix inequality is implied by a quadratic inequality in vectorized variables.

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arXiv2026

Kernel-based identification of nonlinear port-Hamiltonian systems

Port-Hamiltonian systems provide a structured framework for modeling physical systems by explicitly capturing their energy storage, dissipation, and exchange. However, deriving such models often requires detailed physical insight and precise knowledge of system parameters, which may not be available in practice. In this paper, we propose a kernel-based framework for the identification of port-Hamiltonian systems from input-state-output data. In contrast to conventional parametric approaches, the maps defining the port-Hamiltonian system are represented in suitably chosen reproducing kernel Hilbert spaces. This leads to an infinite-dimensional optimization problem over the corresponding function spaces. Our main result establishes a representer theorem that reduces this problem to a tractable finite-dimensional one. Since the reduced problem is non-convex, we further provide an algorithm for its solution and prove its convergence.

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arXiv2026

Data-Driven Robust Model Reference Adaptive Control with Parameter Convergence

This paper provides a data-driven design guaranteeing parameter convergence in model reference adaptive control (MRAC) when the to-be-controlled system is subject to process noise. In the context of MRAC, parameter convergence refers to ensuring convergence of the adaptive gains to a solution of the matching equations, or to an approximate solution when noise is present. In classical MRAC, even small noise may induce parameter drift, thus lacking robustness to noise. Meanwhile, existing robust MRAC methods cannot ensure parameter convergence without imposing excitation conditions on data. A key feature of the proposed framework is to ensure convergence of the adaptive gains to an approximate solution of the matching equations without relying on persistently exciting signals. Furthermore, the matching error can be explicitly characterized as a function of the noise. This explicit characterization allows to establish a necessary and sufficient condition on the noise characteristics under which the limit closed-loop system matrix is Hurwitz. In the noise-free case, the proposed framework results in exact parameter convergence. Notably, as compared to existing methods achieving exact parameter convergence in the noise-free case, the condition on data in the proposed framework is weaker.

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arXiv2026

From time series to dissipativity of linear systems with dynamic supply rates

This paper studies the problem of verifying dissipativity of linear time-invariant (LTI) systems using input-output data. We leverage behavioral systems theory to express dissipativity in terms of quadratic difference forms (QDFs), allowing the study of general dynamic quadratic supply rates. We work under the assumptions that the data-generating system is controllable, and an upper bound is given on its lag. As our main results, we provide sufficient conditions for the data to be informative for dissipativity. We also show that for a specific class of static supply rates, these conditions are both necessary and sufficient. For the latter supply rates, it turns out that certification of dissipativity is only possible from data that enable unique system identification. As auxiliary results, we highlight some properties of QDFs, such as upper bounds on the degree of storage functions.

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arXiv2026

Convergence of energy-based learning in linear resistive networks

Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this direction by analysing a particular energybased learning algorithm, Contrastive Learning, applied to a network of linear adjustable resistors. It is shown that, in this setup, Contrastive Learning is equivalent to projected gradient descent on a convex function with Lipschitz continuous gradient, giving a guarantee of convergence of the algorithm for a range of stepsizes. This convergence result is then extended to a stochastic variant of Contrastive Learning.

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arXiv2025

Experiment design using prior knowledge on controllability and stabilizability

In this paper, we consider the problem of designing input signals for an unknown linear time-invariant system in such a way that the resulting input-state data is suitable for identification or stabilization. We will take into account prior knowledge on system-theoretic properties of the system, in particular, controllability and stabilizability. For this, we extend the notion of universal inputs to incorporate prior knowledge on the system. An input is called universal for identification (resp., stabilization) if, when applied to any system complying with the prior knowledge, it results in data suitable for identification (resp., stabilization) regardless of the initial condition. We provide a full characterization of such universal inputs. In addition, we discuss online experiment design using prior knowledge, and we study cases where this approach results in the shortest possible experiment for identification and stabilization.

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arXiv2025

Chebyshev centers and radii for sets induced by quadratic matrix inequalities

This paper studies sets of matrices induced by quadratic inequalities. In particular, the center and radius of a smallest ball containing the set, called a Chebyshev center and the Chebyshev radius, are studied. In addition, this work studies the diameter of the set, which is the farthest distance between any two elements of the set. Closed-form solutions are provided for a Chebyshev center, the Chebyshev radius, and the diameter of sets induced by quadratic matrix inequalities (QMIs) with respect to arbitrary unitarily invariant norms. Examples of these norms include the Frobenius norm, spectral norm, nuclear norm, Schatten p-norms, and Ky Fan k-norms. In addition, closed-form solutions are presented for the radius of the largest ball within a QMI-induced set. Finally, the paper discusses applications of the presented results in data-driven modeling and control.

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arXiv2025

Data-driven stabilization of polynomial systems using density functions

This paper studies data-driven stabilization of a class of unknown polynomial systems using data corrupted by bounded noise. Existing work addressing this problem has focused on designing a controller and a Lyapunov function so that a certain state-dependent matrix is negative definite, which ensures asymptotic stability of all closed-loop systems compatible with the data. However, as we demonstrate in this paper, considering the negative definiteness of this matrix introduces conservatism, which limits the applicability of current approaches. To tackle this issue, we develop a new method for the data-driven stabilization of polynomial systems using the concept of density functions. The control design consists of two steps. Firstly, a dual Lyapunov theorem is used to formulate a sum of squares program that allows us to compute a rational state feedback controller for all systems compatible with the data. By the dual Lyapunov theorem, this controller ensures that the trajectories of the closed-loop system converge to zero for almost all initial states. Secondly, we propose a method to verify whether the designed controller achieves asymptotic stability of all closed-loop systems compatible with the data. Apart from reducing conservatism of existing methods, the proposed approach can also readily take into account prior knowledge on the system parameters. A key technical result developed in this paper is a new type of S-lemma for a specific class of matrices that, in contrast to the classical S-lemma, avoids the use of multipliers.

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arXiv2025

A new perspective on Willems' fundamental lemma: Universality of persistently exciting inputs

In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that parametrizes all finite trajectories of the system. By the fundamental lemma, inputs that are persistently exciting of sufficiently high order are universal. The main contribution of this work is to prove the converse. Therefore, universality and persistency of excitation are equivalent.

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arXiv2025

Feedback Stabilization of Polynomial Systems: From Model-based to Data-driven Methods

In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system only when the Lyapunov function is radially unbounded, which limits its applicability. To overcome this limitation, we develop a new global stabilization approach that allows a broader class of Lyapunov function candidates. Furthermore, we extend this approach to the data-driven setting, considering Lyapunov function candidates with the same functional structure. Using data corrupted by bounded noise, we derive conditions for constructing globally stabilizing controllers for unknown polynomial systems. Beyond handling noise, the proposed data-driven approach can be readily adapted to incorporate further prior knowledge of system parameters to reduce conservatism. In both approaches, sum-of-squares relaxation is used to ensure computational tractability of the involved conditions.

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arXiv2025

Synthesis of Dissipative Systems Using Input-State Data

This paper deals with the data-driven synthesis of dissipative linear systems in discrete time. We collect finitely many noisy data samples with which we synthesise a controller that makes all systems that explain the data dissipative with respect to a given quadratic supply rate. By adopting the informativity approach, we introduce the notion of informativity for closed-loop dissipativity. Under certain assumptions on the noise and the system, with the help of tools for quadratic matrix inequalities, we provide necessary and sufficient conditions for informativity for closed-loop dissipativity. We also provide a recipe to design suitable controllers by means of data-based linear matrix inequalities. This main result comprises two parts, to account for both the cases that the output matrices are known or unknown. Lastly, we illustrate our findings with an example, for which we want to design a data-driven controller achieving (strict) passivity.

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arXiv2024

Necessary and Sufficient Conditions for Data-driven Model Reference Control

The objective of model reference control is to design a controller that regulates the system's behavior so as to match a specified reference model. This paper investigates necessary and sufficient conditions for model reference control from a data-driven perspective, when only a set of data generated by the system is utilized to directly accomplish the matching. Noiseless and noisy data settings are both considered. Notably, all methods we propose build on the concept of data informativity and do not rely on persistently exciting data.

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