arXiv subjects

Alessio Moreschini

Publications and source records attributed to Alessio Moreschini.

10 recordsLinked to original sources

arXiv2026

Frequency Response of Nonlinear Systems: Notions, Analysis, and Graphical Representation

The invariance principle, through which the steady-state behavior of nonlinear systems was introduced by Isidori and Byrnes, is leveraged in this article to bring forth a unifying characterization of the frequency response of nonlinear systems. We show that, for systems under nonlinear periodic excitations, the frequency response can still be defined as a complex-valued function in a phasor form. However, together with suitable notions of gain and phase functions, we show the existence of another function that completes the frequency response and allows quantifying the distortion introduced by the system in the steady-state output. This nonlinear characterization enabled the representation over input frequency and amplitude of the gain, phase, and distortion produced by the system, via a nonlinear enhancement of the Bode diagrams. This graphical representation of the frequency response is well-suited to performance analysis of a nonlinear system and, furthermore, allows for the formulation of the loop-shaping problem for nonlinear systems.

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arXiv2026

A Functional Learning Approach for Team-Optimal Traffic Coordination

In this paper, we develop a kernel-based policy iteration functional learning framework for computing team-optimal strategies in traffic coordination problems. We consider a multi-agent discrete-time linear system with a cost function that combines quadratic regulation terms and nonlinear safety penalties. Building on the Hilbert space formulation of offline receding-horizon policy iteration, we seek approximate solutions within a reproducing kernel Hilbert space, where the policy improvement step is implemented via a discrete Fr\'echet derivative. We further study the model-free receding-horizon scenario, where the system dynamics are estimated using recursive least squares, followed by updating the policy using rolling online data. The proposed method is tested in signal-free intersection scenarios via both model-based and model-free simulations and validated in SUMO.

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arXiv2025

Globally Stable Discrete Time PID Passivity-based Control of Power Converters: Simulation and Experimental Results

The key idea behind PID Passivity-based Control (PID-PBC) is to leverage the passivity property of PIDs (for all positive gains) and wrap the PID controller around a passive output to ensure global stability in closed-loop. However, the practical applicability of PID-PBC is stymied by two key facts: (i) the vast majority of practical implementations of PIDs is carried-out in discrete time -- discretizing the continuous time dynamical system of the PID; (ii) the well-known problem that passivity is not preserved upon discretization, even with small sampling times. Therefore, two aspects of the PID-PBC must be revisited for its safe practical application. First, we propose a discretization of the PID that ensures its passivity. Second, since the output that is identified as passive for the continuous time system is not necessarily passive for its discrete time version, we construct a new output that ensures the passivity property for the discretization of the system. In this paper, we provide a constructive answer to both issues for the case of power converter models. Instrumental to achieve this objective is the use of the implicit midpoint discretization method -- which is a symplectic integration technique that preserves system invariants. Since the reference value for the output to be regulated in power converters is non-zero, we are henceforth interested in the property of passivity of the incremental model -- currently known as shifted passivity. Therefore, we demonstrate that the resulting discrete-time PID-PBC defines a passive map for the incremental model and establish shifted passivity for the discretized power converter model. Combining these properties, we prove global stability for the feedback interconnection of the power converter with the discretized PID-PBC. The paper also presents simulations and experiments that demonstrate the performance of the proposed discretization.

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arXiv2025

Data-Driven Adjustable Robust Optimization

In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In the first stage, we synthesize an uncertainty set to ensure the feasibility of the problem as much as possible using the collected uncertainty samples. In the second stage, we find the optimal solution while ensuring that the constraints are satisfied under the new uncertainty set. This approach enlarges the feasible state set, at the expense of the risk of possible constraint violation. We analyze two scenarios: one where the uncertainty is non-stochastic, and another where the uncertainty is stochastic but with unknown probability distribution, leading to a distributionally robust optimization problem. In the first case, we scale the uncertainty set and find the best subset that fits the uncertainty samples. In the second case, we employ the Wasserstein metric to quantify uncertainty based on training data, and for polytope uncertainty sets, we further provide a finite program reformulation of the problem. The effectiveness of the proposed methods is demonstrated through an optimal power flow problem.

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arXiv2025

Fault Localisation in Infinite-Dimensional Linear Electrical Networks

We present a novel fault localisation methodology for linear time-invariant electrical networks with infinite-dimensional edge dynamics and uncertain fault dynamics. The theory accommodates instability and also bounded propagation delays in the network. The goal is to estimate the location of a fault along a given network edge, using sensors positioned arbitrarily throughout the network. Passive faults of unknown impedance are considered, along with stable faults of known impedance. To illustrate the approach, we tackle a significant use-case: a multi-conductor transmission line, with dynamics modelled by the Telegrapher's equation, subject to a line-to-ground fault. Frequency-domain insights are used to reformulate the general fault localisation problem into a non-convex scalar optimisation problem, of which the true fault location is guaranteed to be a global minimiser. Numerical experiments are run to quantify localisation performance over a range of fault resistances.

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arXiv2025

Frequency-Domain Bounds for the Multiconductor Telegrapher's Equation

We establish mathematical bounds on the chain, ABCD and immittance matrices of a multiconductor transmission line, based on the Telegrapher's equation. Closed-form expressions for those matrices are also presented. Existing results that hold on the imaginary axis are extended to the complex plane, without reliance on a diagonalizability assumption that is prevalent in the literature. Therefore, the results remain valid under arbitrary arrangements of the conducting wires, which include electrical faults. The analysis ultimately reveals important system-theoretic implications of the Telegrapher's equation, which are of general relevance to control, power systems, and signal processing involving multiconductor transmission lines.

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arXiv2024

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.

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arXiv2023

Krasovskii Passivity for Sampled-data Stabilization and Output Consensus

In this paper, we establish the novel concept of Krasovskii passivity for sampled discrete-time nonlinear systems, enabling Krasovskii-passivity-based control design under sampling. We consider two separate control objectives: stabilization and output consensus, where the latter is studied under the presence of an unknown constant disturbance. Inspired by methodologies in the continuous-time case, we develop sampled-data control schemes for each control objective based on Krasovskii passivity. The proposed sampled discrete-time controllers are respectively validated through simulations on a DC microgrid of boost converters and a DC microgrid of buck converters whose continuous-time models and their implicit midpoint discretizations are Krasovskii passive in each time scale.

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arXiv2022

Quaternion-based attitude stabilization via discrete-time IDA-PBC

In this paper, we propose a new sampled-data controller for stabilization of the attitude dynamics at a desired constant configuration. The design is based on discrete-time interconnection and damping assignment (IDA) passivity-based control (PBC) and the recently proposed Hamiltonian representation of discrete-time nonlinear dynamics. Approximate solutions are provided with simulations illustrating performances.

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arXiv2021

On feedback passivation under sampling

In this paper we show that feedback passivation under sampling can be preserved under digital control through the redefinition of a passifying output map which depends on the sampling period. The design is constructive and approximate solutions make sense. The procedure is applied to port Hamiltonian dynamics and Interconnection and Damping Assignment feedback. Performances are illustrated over the gravity pendulum example.

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