arXiv subjects

M. Kanat Camlibel

Publications and source records attributed to M. Kanat Camlibel.

At least 19 recordsLinked to original sources

arXiv2026

Fragility Analysis of Data-Driven Feedback Gains

For linear time-invariant systems, input-state data collected during an open-loop experiment can remedy the lack of knowledge of system parameters. However, such data do not contain information about other system uncertainties such as feedback perturbations. In this paper, we study the effect of additive perturbations on control parameters in a data-based setting. To this end, we parameterize the set of quadratically stabilizing feedback gains obtained from noisy input-state data. We study the case where a stabilizing data-driven feedback gain is extremely sensitive to feedback perturbations, i.e., a small perturbation in the control parameters, no matter how small, could destabilize the unknown true system. We refer to this case as extreme fragility for which we provide a full characterization. We also present necessary and sufficient conditions for the case where the closed-loop system is completely immune to feedback perturbations. For the general case where the feedback gain is neither extremely fragile nor immune, we provide a measure by which one can quantize the control fragility directly based on the collected data. We also study the problem of designing the least fragile data-driven feedback gain. The results are presented in terms of linear matrix inequalities and semi-definite programs.

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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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arXiv2025

Data-driven Synchronization for Network Systems with Noiseless Data

For a collection of homogeneous LTI systems that is interconnected by a protocol, given the network topology and the system model, one may obtain a feedback gain to synchronize the network. However, the model-based methods cannot be applied in case the system model is unknown. Therefore, in this paper, we study the data-driven synchronization problem for homogeneous networks. In particular, given a collection of LTI systems, we collect the input-state data from one individual system. Then, given the network topology, we provide data-based necessary and sufficient conditions for synchronizability. Once the conditions are satisfied, one can also obtain a feedback gain directly from data to synchronize the network with the corresponding design method provided in this paper. Finally, we illustrate our results with a numerical simulation.

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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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arXiv2024

The shortest experiment for linear system identification

This paper is concerned with the following problem: given an upper bound of the state-space dimension and lag of a linear time-invariant system, design a sequence of inputs so that the system dynamics can be recovered from the resulting input-output data. As our main result we propose a new online experiment design method, meaning that the selection of the inputs is iterative and guided by data samples collected in the past. We show that this approach leads to the shortest possible experiments for linear system identification. In terms of sample complexity, the proposed method outperforms offline methods based on persistency of excitation as well as existing online experiment design methods.

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arXiv2023

A Real-Time Balancing Market Optimization with Personalized Prices: From Bilevel to Convex

This paper studies the static economic optimization problem of a system with a single aggregator and multiple prosumers in a Real-Time Balancing Market (RTBM). The aggregator, as the agent responsible for portfolio balancing, needs to minimize the cost for imbalance satisfaction in real-time by proposing a set of optimal personalized prices to the prosumers. On the other hand, the prosumers, as price taker and self-interested agents, want to maximize their profit by changing their supplies or demands and providing flexibility based on the proposed personalized prices. We model this problem as a bilevel optimization problem. We first show that the optimal solution of this bilevel optimization problem can be found by solving an equivalent convex problem. In contrast to the state-of-the-art Mixed-Integer Programming (MIP)-based approach to solve bilevel problems, this convex equivalent has very low computation time and is appropriate for real-time applications. Next, we compare the optimal solutions of the proposed personalized scheme and a uniform pricing scheme. We prove that, under the personalized pricing scheme, more prosumers contribute to the RTBM and the aggregator's cost is less. Finally, we verify the analytical results of this work by means of numerical case studies and simulations.

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arXiv2023

Quadratic matrix inequalities with applications to data-based control

This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, bounded, or has nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of ``structured" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma, that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMI's can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller, and also leads to explicit formulas for data-guided feedback gains.

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arXiv2023

The informativity approach to data-driven analysis and control

The goal of this paper is to provide a tutorial on the so-called informativity framework for direct data-driven analysis and control. This framework achieves certified data-based analysis and control by assessing system properties and determining controllers for sets of systems unfalsified by the data. We will first introduce the informativity approach at an abstract level. Thereafter, we will report case studies where we highlight the strength of the framework in the context of various problems involving both noiseless and noisy data. In particular, we will treat controllability and stabilizability, and stabilization, linear quadratic regulation, and tracking and regulation using exact input-state measurements. Thereafter, we will treat dissipativity analysis, stabilization, and H_inf control using noisy input-state data. Finally, we will study dynamic measurement feedback stabilization using noisy input-output data. We will provide several examples to illustrate the approach. In addition, we will highlight the main tools underlying the framework, such as quadratic matrix inequalities in robust control and quadratic difference forms in behavioral systems theory.

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arXiv2022

Port-Hamiltonian systems and monotonicity

The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to maximal cyclically monotone relations, together with their generating functions. This gives rise to new classes of incrementally port-Hamiltonian systems, with examples stemming from physical systems modeling as well as from convex optimization. An in-depth treatment is given of the composition of maximal monotone and maximal cyclically monotone relations, where in the latter case the resulting maximal cyclically monotone relation is shown to be computable through the use of generating functions. Furthermore, connections are discussed with incremental versions of passivity, and it is shown how incrementally port-Hamiltonian systems with strictly convex Hamiltonians are (maximal) equilibrium independent passive. Finally, the results on compositionality of monotone relations are employed for a convex optimization approach to the computation of the equilibrium of interconnected incrementally port-Hamiltonian systems.

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arXiv2022

A behavioral approach to data-driven control with noisy input-output data

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

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arXiv2022

From data to reduced-order models via moment matching

A new method for data-driven interpolatory model reduction is presented in this paper. Using the so-called data informativity perspective, we define a framework that enables the computation of moments at given (possibly complex) interpolation points based on time-domain input-output data only, without explicitly identifying the high-order system. Instead, by characterizing the set of all systems explaining the data, necessary and sufficient conditions are provided under which all systems in this set share the same moment at a given interpolation point. Moreover, these conditions allow for explicitly computing these moments. Reduced-order models are then derived by employing a variation of the classical rational interpolation method. The condition to enforce moment matching model reduction with prescribed poles is also discussed as a means to obtain stable reduced-order models. An example of an electrical circuit illustrates this framework.

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arXiv2022

On eigenvectors of convex processes in non-pointed cones

Spectral analysis of convex processes has led to many results in the analysis of differential inclusions with a convex process. In particular the characterization of eigenvalues with eigenvectors in a given cone has led to results on controllability and stabilizability. However, these characterizations can handle only pointed cones. This paper will generalize all known results characterizing eigenvalues of convex processes with eigenvectors in a given cone. In addition, we reveal the link between the assumptions on our main theorem and classical geometric control theory.

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arXiv2022

From data to reduced-order models via generalized balanced truncation

This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin projection to all systems explaining the data characterized in a large-dimensional quadratic matrix inequality (QMI) can again be characterized in a lower-dimensional QMI. Next, we develop a data-driven generalized balanced truncation method that relies on two steps. First, we provide necessary and sufficient conditions such that systems explaining the data have common generalized Gramians. Second, these common generalized Gramians are used to construct projection matrices that allow to characterize a class of reduced-order models via generalized balanced truncation in terms of a lower-dimensional QMI by applying the data reductionconcept. Additionally, we present alternative procedures to compute a priori and a posteriori upper bounds with respect to the true system generating the data. Finally, the proposed techniques are illustrated by means of application to an example of a system of a cart with a double-pendulum.

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