arXiv subjects

Giulio Fattore

Publications and source records attributed to Giulio Fattore.

7 recordsLinked to original sources

arXiv2026

Identification of forward models: a nonparametric approach

In this paper we propose a new kernel-based method for the identification of the impulse responses of forward models. The resulting estimator leads to a nonlinear Tikhonov regularization problem for which we prove the existence of a solution. The latter result makes legitimate to approximate the forward model through a high-order Moving Average with eXogenous input (MAX) model, i.e. the numerical solution found using this model introduces only a negligible bias in the estimate. The optimization of the marginal likelihood to estimate the kernel hyperparameters is also taken into account. Since there does not exist a closed-form expression for the marginal likelihood, we present an evaluation method that relies on the Laplace approximation of the marginal likelihood. Finally, some numerical experiments are discussed to show the effectiveness of the proposed method.

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arXiv2026

Distributed Observer Design for Discrete-Time LTI Systems via Jordan Canonical Form

This paper addresses the problem of distributed state estimation for discrete-time linear time-invariant systems. Building on the framework proposed in Gao & Yang (2025), we exploit the Jordan canonical form of the system matrix to develop two distributed estimation schemes that ensure asymptotic convergence of local estimates to the true system state. In both approaches, each node reconstructs the components of the state that are locally detectable for it via a Luenberger observer, while employing a consensus-based mechanism to estimate the components that are not directly detectable. The first scheme relies on local observers whose dimension matches that of the original state vector; however, its applicability requires the satisfaction of a large set of inequalities. The second scheme, in contrast, can be implemented under less restrictive conditions, but results in observers of increased (augmented) order. For both methods, we derive necessary and sufficient conditions - expressed in terms of the eigenvalues of the system matrix and certain submatrices of the communication network Laplacian - that guarantee the existence of a distributed observer achieving asymptotically accurate estimation. Compared to Gao & Yang (2025), the proposed approaches offer greater flexibility in the selection of coupling gains and impose less stringent solvability conditions.

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arXiv2026

Distributed State Estimation of Discrete-Time LTI Systems via Jordan Canonical Representation

In this paper, we address the problem of distributed state estimation for a discrete-time, linear time-invariant system. Building on the framework proposed in [2], we exploit the Jordan canonical form of the system matrix to develop a distributed estimation scheme that ensures the asymptotic convergence of the local state estimates to the true system state. The proposed approach relies on the idea that each node reconstructs the components of the system state that are detectable for it through a local Luenberger observer, while employing a consensus-based strategy to estimate the undetectable components. Necessary and sufficient conditions for the existence of a distributed observer that guarantees asymptotic estimation accuracy are derived. Compared with the previous work [2], the proposed design offers greater flexibility in the selection of the coupling gains and leads to a less restrictive set of conditions for solvability.

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arXiv2025

Data-Driven Distributed Output Synchronization of Heterogeneous Discrete-Time Multi-Agent Systems

In this paper, we assume that an autonomous exosystem generates a reference output, and we consider the problem of designing a distributed data-driven control law for a family of discrete-time heterogeneous LTI agents, connected through a directed graph, in order to synchronize the agents' outputs to the reference one. The agents of the network are split into two categories: leaders, with direct access to the exosystem output, and followers, that only receive information from their neighbors. All agents aim to achieve output synchronization by means of a state feedback that makes use of their own states as well as of an estimate of the exogenous system state, provided by an internal state observer. Such observer has a different structure for leaders and followers. Necessary and sufficient conditions for the existence of a solution are first derived in the model-based set-up and then in a data-driven context. An example illustrates both the implementation procedure and the performance of the proposed approach.

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arXiv2024

A kernel-based PEM estimator for forward models

This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with a high-order stable ARX model. However, such choice induces a certain undesired prior information in the system that we want to estimate. To overcome this issue, we propose a new kernel-based paradigm which is formulated directly in terms of the impulse responses of the forward model and leading to the identification of a high-order MAX model. The most challenging step is the estimation of the kernel hyperparameters optimizing the marginal likelihood. The latter, indeed, does not admit a closed form expression. We propose a method for evaluating the marginal likelihood which makes possible the hyperparameters estimation. Finally, some numerical results showing the effectiveness of the method are presented.

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arXiv2024

A data-driven approach to UIO-based fault diagnosis

In this paper we propose a data-driven approach to the design of a residual generator, based on a dead-beat unknown-input observer, for linear time-invariant discrete-time state-space models, whose state equation is affected both by disturbances and by actuator faults. We first review the modelbased conditions for the existence of such a residual generator, and then prove that under suitable assumptions on the collected historical data, we are both able to determine if the problem is solvable and to identify the matrices of a possible residual generator. We propose an algorithm that, based only on the collected data (and not on the system description), is able to perform both tasks. An illustrating example and some remarks on limitations and possible extensions of the current results conclude the paper.

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arXiv2023

Optimal Time-Invariant Distributed Formation Tracking for Second-Order Multi-Agent Systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

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