arXiv subjects

Giordano Scarciotti

Publications and source records attributed to Giordano Scarciotti.

15 recordsLinked to original sources

arXiv2026

A polynomial approximation scheme for nonlinear model reduction by moment matching

We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators.

math.OC↗

arXiv2026

On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation

Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.

eess.SY↗

arXiv2026

Approximate Simulation-based Hierarchical Control of Nonlinear Systems

Controlling complex dynamical systems to satisfy sophisticated specifications remains a significant challenge in modern engineering. A promising approach to this problem is the approximate simulation-based hierarchical control (ASHC) technique. In this method, a simplified representation of the complex system, called the abstract system, is first designed and controlled. An interface function is then designed to translate the control law into the input of the complex system, thereby achieving approximate control synthesis. However, most existing results in ASHC are only for linear systems. This paper proposes a constructive method for solving the ASHC problem for nonlinear systems. To this end, we propose invariance equation-based methods to achieve the two classical requirements of the ASHC technique, namely the bounded output discrepancy and the $m$-relation. We then study the solvability conditions of the problem and summarise the overall design procedures. We illustrate the results with a practical example, providing step-by-step solutions to the ASHC problem of a DC-to-DC Ćuk converter.

eess.SY↗

arXiv2026

Interconnection-based Model Reduction for Linear Hybrid Systems

In this paper, we address the model reduction problem for linear hybrid systems via the interconnection-based technique called moment matching. We consider two classical interconnections, namely the direct and swapped interconnections, in the hybrid setting, and we present families of reduced-order models for each interconnection via a hybrid characterisation of the steady-state responses. By combining the results for each interconnection, the design of a reduced-order model that achieves moment matching simultaneously for both interconnections is studied. In addition, we show that the presented results have simplified counterparts when the jumps of the hybrid system are periodic. A numerical simulation is finally given to illustrate the results.

eess.SY↗

arXiv2025

Bridging Abstraction-Based Hierarchical Control and Moment Matching: A Conceptual Unification

In this paper, we establish a relation between approximate-simulation-based hierarchical control (ASHC) and moment matching techniques, and build a conceptual bridge between these two frameworks. To this end, we study the two key requirements of the ASHC technique, namely the bounded output discrepancy and the $M$-relation, through the lens of moment matching. We show that, in the linear time-invariant case, both requirements can be interpreted in the moment matching perspective through certain system interconnection structures. Building this conceptual bridge provides a foundation for cross-pollination of ideas between these two frameworks.

eess.SY↗

arXiv2025

One Equation to Rule Them All -- Part I: Direct Data-Driven Cascade Stabilisation

In this article we present a framework for direct data-driven control for general problems involving interconnections of dynamical systems. We first develop a method to determine the solution of a Sylvester equation from data. Such solution is used to describe a subspace that plays a role in a large variety of problems. We then provide an error analysis of the impact that noise has on this solution. This is a crucial contribution because, thanks to the interconnection approach developed throughout the article, we are able to track how the noise propagates at each stage, and thereby provide bounds on the final designs. Among the many potential problems that can be solved with this framework, we focus on three representatives: cascade stabilisation, model order reduction, and output regulation. This manuscript studies the first problem, while the companion Part II addresses the other two. For each of these settings we show how the problems can be recast in our framework. In the context of cascade stabilisation, we consider the 2-cascade problem, the effect of noise through the cascade, as well as N-cascade case, and we demonstrate that our proposed method is data efficient. The proposed designs are illustrated by means of a numerical example.

eess.SY↗

arXiv2025

One Equation to Rule Them All -- Part II: Direct Data-Driven Reduction and Regulation

The Sylvester equation underpins a wide spectrum of control synthesis and systems analysis tools associated with cascade interconnections. In the preceding Part I [1] of this article, it was shown that such an equation can be reformulated using data, enabling the production of a collection of data-driven stabilisation procedures. In this second part of the article, we continue to develop the framework established in Part I to solve two important control-theoretic problems: model order reduction and output regulation. For the model order reduction problem we provide a solution from input-state measurements, from input-output measurements, and we study the effect of the noise. For the output regulation problem, we provide data-driven solutions for the static and dynamic feedback problem. The proposed designs are illustrated by means of examples.

eess.SY↗

arXiv2025

Data-Driven Model Reduction by Moment Matching for Linear and Nonlinear Parametric Systems

Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment of linear and nonlinear parametric systems are proposed. These approximations are exploited to construct families of parametric reduced-order models that match the approximate parametric moment of the system to be reduced and preserve key system properties such as asymptotic stability and dissipativity. The use of the model reduction methods is illustrated by means of a parametric benchmark model for the linear case and a large-scale wind farm model for the nonlinear case. In the illustration, a comparison of the proposed approximation methods is drawn and their advantages/disadvantages are discussed.

eess.SY↗

arXiv2025

Output Regulation of Linear Systems with Non-periodic Non-smooth Exogenous Signals

We address the output regulation problem of linear systems with non-smooth and non-periodic exogenous signals. Specifically, we first formulate and solve the full-information problem by designing a state-feedback controller. We study the solvability of the regulator equations, providing a new non-resonance condition. We then focus on the error-feedback problem, for which we design a (non-robust) internal model leveraging the concept of canonical realisation and applying a high-gain method for the stabilisation of the closed-loop system under the minimum-phase assumption. Finally, we study the regulation problem involving model parameter uncertainties. Drawing ideas from both hybrid and time-varying (smooth) output regulation, we propose two methods to establish an internal model that is robust to uncertainties. The first method is an extension of the hybrid internal model, while the second relies on a new concept of immersion. In this non-smooth case, the immersion is established based on integrals rather than derivatives. The effectiveness of the proposed solutions is illustrated by a circuit regulation example.

eess.SY↗

arXiv2025

Steady-State Cascade Operators and their Role in Linear Control, Estimation, and Model Reduction Problems

Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We conduct here a comprehensive study of these operators and their relevant system-theoretic properties. The general theory is leveraged to delineate both known and new design methodologies for control and observation of cascades, and to characterize structural properties of reduced models. Several entirely new designs arise from this systematic categorization, including new recursive and low-gain design frameworks for observation of cascaded systems. The benefits of the results beyond the linear time-invariant setting are demonstrated through preliminary extensions for nonlinear systems, with an outlook towards the development of a similarly comprehensive nonlinear theory.

eess.SY↗

arXiv2024

Model Order Reduction of Large-Scale Wind Farms: A Data-Driven Approach

This paper proposes a data-driven algorithm for model order reduction (MOR) of large-scale wind farms and studies the effects that the obtained reduced-order model (ROM) has when this is integrated into the power grid. With respect to standard MOR methods, the proposed algorithm has the advantages of having low computational complexity and not requiring any knowledge of the high order model. Using time-domain measurements, the obtained ROM achieves the moment matching conditions at selected interpolation points (frequencies). With respect to the state of the art, the method achieves the so-called two-sided moment matching, doubling the accuracy by doubling the interpolated points. The proposed algorithm is validated on a combined model of a 200-turbine wind farm (which is reduced) interconnected to the IEEE 14-bus system (which represents the unreduced study area) by comparing the full-order model and the reduced-order model in terms of their Bode plots, eigenvalues and the point of common coupling voltages in extensive fault scenarios of the integrated power system.

eess.SY↗

arXiv2022

Data-Driven Model Reduction by Two-Sided Moment Matching

In this brief paper, we propose a time-domain data-driven method for model order reduction by two-sided moment matching for linear systems. An algorithm that asymptotically approximates the matrix product $ΥΠ$ from time-domain samples of the so-called two-sided interconnection is provided. Exploiting this estimated matrix, we determine the unique reduced-order model of order $ν$, which asymptotically matches the moments at $2 ν$ distinct interpolation points. Furthermore, we discuss the impact that certain disturbances and data distortions may have on the algorithm. Finally, we illustrate the use of the proposed methodology by means of a benchmark model.

eess.SY↗

arXiv2022

Stochastic Relative Degree and Path-wise Control of Nonlinear Stochastic Systems

We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the dynamics to a stochastic normal form. The normal form is instrumental for the design of a state-feedback control which linearises and makes the dynamics deterministic. We observe that this control is idealistic, i.e. it is not practically implementable because it employs a feedback of the Brownian motion (which is never available) to cancel the noise. Using the idealistic control as a starting point, we introduce a hybrid control architecture which achieves \emph{practical} path-wise control. This hybrid controller uses measurements of the state to perform periodic compensations for the noise contribution to the dynamics. We prove that the hybrid controller retrieves the idealistic performances in the limit as the compensating period approaches zero. We address the problem of asymptotic output tracking, solving it in the idealistic and in the practical framework. We finally validate the theory by means of a numerical example.

eess.SY↗

arXiv2021

On Moment Matching for Stochastic Systems

In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of models which achieve moment matching. However, differently from the deterministic case, these reduced-order models cannot be considered "simpler" because of the high computational cost paid to determine the moment. To overcome this difficulty, we relax the moment matching problem in two different ways and we present two classes of reduced-order models which, approximately matching the stochastic moment, are computationally tractable.

eess.SY↗

arXiv2021

Output Regulation of Linear Stochastic Systems

We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but non-causal, asymptotic regulation. A characterisation of the problem solvability is deduced. We point out that the ideal problems cannot be solved in practice because they unrealistically require that the Brownian motion affecting the system is available for feedback. Drawing from the ideal solution, we formulate and solve approximate versions of the full-information and output-feedback problems, which do not yield perfect asymptotic tracking but can be solved in a realistic scenario. These solutions rely on two key ideas: first we introduce a discrete-time a-posteriori estimator of the variations of the Brownian motion obtained causally by sampling the system state or output; second we introduce a hybrid state observer and a hybrid regulator scheme which employ the estimated Brownian variations. The approximate solution tends to the ideal as the sampling period tends to zero. The proposed theory is validated by the regulation of a circuit subject to electromagnetic noise.

eess.SY↗