arXiv subjects

Fabrizio Dabbene

Publications and source records attributed to Fabrizio Dabbene.

At least 37 records · Page 2Linked to original sources

arXiv2025

A control system framework for counterfactuals: an optimization based approach

Counterfactuals are a concept inherited from the field of logic and in general attain to the existence of causal relations between sentences or events. In particular, this concept has been introduced also in the context of interpretability in artificial intelligence, where counterfactuals refer to the minimum change to the feature values that changes the prediction of a classification model. The artificial intelligence framework of counterfactuals is mostly focused on machine learning approaches, typically neglecting the physics of the variables that determine a change in class. However, a theoretical formulation of counterfactuals in a control system framework - i.e., able to account for the mechanisms underlying a change in class - is lacking. To fill this gap, in this work we propose an original control system, physics-informed, theoretical foundation for counterfactuals, by means of the formulation of an optimal control problem. We apply the proposed methodology to a general glucose-insulin regulation model and results appear promising and pave the way to the possible integration with artificial intelligence techniques, with the aim of feeding machine learning models with the physics knowledge acquired through the system framework.

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arXiv2024

Power minimization and resource allocation in HetNets with uncertain channel-gains

We propose an optimization problem to minimize the base stations transmission powers in OFDMA heterogeneous networks, while respecting users' individual throughput demands. The decision variables are the users' working bandwidths, their association, and the base stations transmission powers. To deal with wireless channel uncertainty, the channel gains are treated as random variables respecting a log-normal distribution, leading to a non-convex chance constrained mixed-integer optimization problem, which is then formulated as a mixed-integer Robust Geometric Program. The efficacy of the proposed method is shown in a real-world scenario of a large European city.

math.OC↗

arXiv2024

Combining Off-White and Sparse Black Models in Multi-step Physics-based Systems Identification -- EXTENDED VERSION

In this paper, we propose a unified framework for identifying interpretable nonlinear dynamical models that preserve physical properties. The proposed approach integrates physical principles with black-box basis functions to compensate for unmodeled dynamics, ensuring accuracy over long prediction horizons and computational efficiency. Additionally, we introduce penalty terms to enforce physical consistency and stability during training. We provide a comprehensive analysis of theoretical properties related to multi-step nonlinear system identification, establishing bounds on parameter estimation errors and conditions for gradient stability and sparsity recovery. The proposed framework demonstrates significant potential for improving model accuracy and reliability in various engineering applications, making a substantial step towards the effective use of combined off-white and sparse black models in system identification. The effectiveness of the proposed approach is demonstrated on a nonlinear system identification benchmark.

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arXiv2024

Measured-state conditioned recursive feasibility for stochastic model predictive control

In this paper, we address the problem of designing stochastic model predictive control (MPC) schemes for linear systems affected by unbounded disturbances. The contribution of the paper is twofold. First, motivated by the difficulty of guaranteeing recursive feasibility in this framework, due to the nonzero probability of violating chance-constraints in the case of unbounded noise, we introduce the novel definition of measured-state conditioned recursive feasibility in expectation. Second, we construct a stochastic MPC scheme, based on the introduction of ellipsoidal probabilistic reachable sets, which implements a closed-loop initialization strategy, i.e., the current measured-state is employed for initializing the optimization problem. This new scheme is proven to satisfy the novel definition of recursive feasibility, and its superiority with respect to open-loop initialization schemes, arising from the fact that one never neglects the information brought by the current measurement, is shown through numerical examples.

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arXiv2024

A Joint Optimization Approach for Power-Efficient Heterogeneous OFDMA Radio Access Networks

Heterogeneous networks have emerged as a popular solution for accommodating the growing number of connected devices and increasing traffic demands in cellular networks. While offering broader coverage, higher capacity, and lower latency, the escalating energy consumption poses sustainability challenges. In this paper a novel optimization approach for OFDMA heterogeneous networks is proposed to minimize transmission power while respecting individual users throughput constraints. The problem is formulated as a mixed integer geometric program, and optimizes at once multiple system variables such as user association, working bandwidth, and base stations transmission powers. Crucially, the proposed approach becomes a convex optimization problem when user-base station associations are provided. Evaluations in multiple realistic scenarios from the production mobile network of a major European operator and based on precise channel gains and throughput requirements from measured data validate the effectiveness of the proposed approach. Overall, our original solution paves the road for greener connectivity by reducing the energy footprint of heterogeneous mobile networks, hence fostering more sustainable communication systems.

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arXiv2024

CONFIDERAI: a novel CONFormal Interpretable-by-Design score function for Explainable and Reliable Artificial Intelligence

Everyday life is increasingly influenced by artificial intelligence, and there is no question that machine learning algorithms must be designed to be reliable and trustworthy for everyone. Specifically, computer scientists consider an artificial intelligence system safe and trustworthy if it fulfills five pillars: explainability, robustness, transparency, fairness, and privacy. In addition to these five, we propose a sixth fundamental aspect: conformity, that is, the probabilistic assurance that the system will behave as the machine learner expects. In this paper, we present a methodology to link conformal prediction with explainable machine learning by defining a new score function for rule-based classifiers that leverages rules predictive ability, the geometrical position of points within rules boundaries and the overlaps among rules as well, thanks to the definition of a geometrical rule similarity term. Furthermore, we address the problem of defining regions in the feature space where conformal guarantees are satisfied, by exploiting the definition of conformal critical set and showing how this set can be used to achieve new rules with improved performance on the target class. The overall methodology is tested with promising results on several datasets of real-world interest, such as domain name server tunneling detection or cardiovascular disease prediction.

cs.LG↗

arXiv2024

A novel mathematical model for predicting the benefits of physical activity on type 2 diabetes progression

Despite the well-acknowledged benefits of physical activity for type 2 diabetes (T2D) prevention, the literature surprisingly lacks validated models able to predict the long-term benefits of exercise on T2D progression and support personalized risk prediction and prevention. To bridge this gap, we developed a novel mathematical model that formalizes the link between exercise and short- and long-term glucose-insulin dynamics to predict the benefits of regular exercise on T2D progression. The model quantitatively captured the dose-response relationship (larger benefits with increasing intensity and/or duration of exercise), it consistently reproduced the benefits of clinical guidelines for diabetes prevention, and it accurately predicted persistent benefits following interruption of physical activity, in line with real-world evidence from the literature. These results are encouraging and can be the basis for future development of decision support tools able to assist patients and clinicians in tailoring preventive lifestyle interventions.

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arXiv2024

Conformal Predictions for Probabilistically Robust Scalable Machine Learning Classification

Conformal predictions make it possible to define reliable and robust learning algorithms. But they are essentially a method for evaluating whether an algorithm is good enough to be used in practice. To define a reliable learning framework for classification from the very beginning of its design, the concept of scalable classifier was introduced to generalize the concept of classical classifier by linking it to statistical order theory and probabilistic learning theory. In this paper, we analyze the similarities between scalable classifiers and conformal predictions by introducing a new definition of a score function and defining a special set of input variables, the conformal safety set, which can identify patterns in the input space that satisfy the error coverage guarantee, i.e., that the probability of observing the wrong (possibly unsafe) label for points belonging to this set is bounded by a predefined $\varepsilon$ error level. We demonstrate the practical implications of this framework through an application in cybersecurity for identifying DNS tunneling attacks. Our work contributes to the development of probabilistically robust and reliable machine learning models.

stat.ML↗

arXiv2023

One-shot backpropagation for multi-step prediction in physics-based system identification -- EXTENDED VERSION

The aim of this paper is to present a novel physics-based framework for the identification of dynamical systems, in which the physical and structural insights are reflected directly into a backpropagation-based learning algorithm. The main result is a method to compute in closed form the gradient of a multi-step loss function, while enforcing physical properties and constraints. The derived algorithm has been exploited to identify the unknown inertia matrix of a space debris, and the results show the reliability of the method in capturing the physical adherence of the estimated parameters.

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arXiv2023

Probabilistic Safety Regions Via Finite Families of Scalable Classifiers

Supervised classification recognizes patterns in the data to separate classes of behaviours. Canonical solutions contain misclassification errors that are intrinsic to the numerical approximating nature of machine learning. The data analyst may minimize the classification error on a class at the expense of increasing the error of the other classes. The error control of such a design phase is often done in a heuristic manner. In this context, it is key to develop theoretical foundations capable of providing probabilistic certifications to the obtained classifiers. In this perspective, we introduce the concept of probabilistic safety region to describe a subset of the input space in which the number of misclassified instances is probabilistically controlled. The notion of scalable classifiers is then exploited to link the tuning of machine learning with error control. Several tests corroborate the approach. They are provided through synthetic data in order to highlight all the steps involved, as well as through a smart mobility application.

stat.ML↗

arXiv2022

3D Map Reconstruction of an Orchard using an Angle-Aware Covering Control Strategy

In the last years, unmanned aerial vehicles are becoming a reality in the context of precision agriculture, mainly for monitoring, patrolling and remote sensing tasks, but also for 3D map reconstruction. In this paper, we present an innovative approach where a fleet of unmanned aerial vehicles is exploited to perform remote sensing tasks over an apple orchard for reconstructing a 3D map of the field, formulating the covering control problem to combine the position of a monitoring target and the viewing angle. Moreover, the objective function of the controller is defined by an importance index, which has been computed from a multi-spectral map of the field, obtained by a preliminary flight, using a semantic interpretation scheme based on a convolutional neural network. This objective function is then updated according to the history of the past coverage states, thus allowing the drones to take situation-adaptive actions. The effectiveness of the proposed covering control strategy has been validated through simulations on a Robot Operating System.

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arXiv2021

Prediction error quantification through probabilistic scaling -- EXTENDED VERSION

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.

math.ST↗

arXiv2021

On the Design of Structured Stabilizers for LTI Systems

Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback design. Leveraging on the Projection Lemma, this work presents a new solution to a class of state-feedback control problems, in which the controller is constrained to belong to a given linear space. We show through extensive discussion and numerical examples that our approach leads to several advantages with respect to existing methods: first, it is computationally efficient; second, it is less conservative than previous methods, since it relaxes the requirement of restricting the Lyapunov matrix to a block-diagonal form.

math.OC↗

arXiv2021

Chance constrained sets approximation: A probabilistic scaling approach -- EXTENDED VERSION

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating sets of given complexity. A probabilistic scaling procedure then allows to rescale these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problem in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems.

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arXiv2020

Learning hidden influences in large-scale dynamical social networks: A data-driven sparsity-based approach

Interpersonal influence estimation from empirical data is a central challenge in the study of social structures and dynamics. Opinion dynamics theory is a young interdisciplinary science that studies opinion formation in social networks and has a huge potential in applications, such as marketing, advertisement and recommendations. The term social influence refers to the behavioral change of individuals due to the interactions with others in a social system, e.g. organization, community, or society in general. The advent of the Internet has made a huge volume of data easily available that can be used to measure social influence over large populations. Here, we aim at qualitatively and quantitatively infer social influence from data using a systems and control viewpoint. First, we introduce some definitions and models of opinions dynamics and review some structural constraints of online social networks, based on the notion of sparsity. Then, we review the main approaches to infer the network's structure from a set of observed data. Finally, we present some algorithms that exploit the introduced models and structural constraints, focusing on the sample complexity and computational requirements.

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arXiv2020

Computationally efficient stochastic MPC: a probabilistic scaling approach

In recent years, the increasing interest in Stochastic model predictive control (SMPC) schemes has highlighted the limitation arising from their inherent computational demand, which has restricted their applicability to slow-dynamics and high-performing systems. To reduce the computational burden, in this paper we extend the probabilistic scaling approach to obtain low-complexity inner approximation of chance-constrained sets. This approach provides probabilistic guarantees at a lower computational cost than other schemes for which the sample complexity depends on the design space dimension. To design candidate simple approximating sets, which approximate the shape of the probabilistic set, we introduce two possibilities: i) fixed-complexity polytopes, and ii) $\ell_p$-norm based sets. Once the candidate approximating set is obtained, it is scaled around its center so to enforce the expected probabilistic guarantees. The resulting scaled set is then exploited to enforce constraints in the classical SMPC framework. The computational gain obtained with the proposed approach with respect to the scenario one is demonstrated via simulations, where the objective is the control of a fixed-wing UAV performing a monitoring mission over a sloped vineyard.

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arXiv2020

A probabilistic validation approach for penalty function design in Stochastic Model Predictive Control

In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either independence nor Gaussianity. We revisit the rather classical approach based on penalty functions, with the aim of designing a control scheme that meets some given probabilistic specifications. The main difference with previous approaches is that we do not recur to the notion of probabilistic recursive feasibility, and hence we do not consider separately the unfeasible case. In particular, two probabilistic design problems are envisioned. The first randomization problem aims to design \textit{offline} the constraint set tightening, following an approach inherited from tube-based MPC. For the second probabilistic scheme, a specific probabilistic validation approach is exploited for tuning the penalty parameter, to be selected \textit{offline} among a finite-family of possible values. The simple algorithm here proposed allows designing a \textit{single} controller, always guaranteeing feasibility of the online optimization problem. The proposed method is shown to be more computationally tractable than previous schemes. This is due to the fact that the sample complexity for both probabilistic design problems depends on the prediction horizon in a logarithmic way, unlike scenario-based approaches which exhibit linear dependence. The efficacy of the proposed approach is demonstrated with a numerical example.

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arXiv2019

A Physics-Based Attack Detection Technique in Cyber-Physical Systems: A Model Predictive Control Co-Design Approach

In this paper a novel approach to co-design controller and attack detector for nonlinear cyber-physical systems affected by false data injection (FDI) attack is proposed. We augment the model predictive controller with an additional constraint requiring the future---in some steps ahead---trajectory of the system to remain in some time-invariant neighborhood of a properly designed reference trajectory. At any sampling time, we compare the real-time trajectory of the system with the designed reference trajectory, and construct a residual. The residual is then used in a nonparametric cumulative sum (CUSUM) anomaly detector to uncover FDI attacks on input and measurement channels. The effectiveness of the proposed approach is tested with a nonlinear model regarding level control of coupled tanks.

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