arXiv subjects

Valentina Breschi

Publications and source records attributed to Valentina Breschi.

At least 37 records · Page 2Linked to original sources

arXiv2025

Insights into the explainability of Lasso-based DeePC for nonlinear systems

Data-enabled Predictive Control (DeePC) has recently gained the spotlight as an easy-to-use control technique that allows for constraint handling while relying on raw data only. Initially proposed for linear time-invariant systems, several DeePC extensions are now available to cope with nonlinear systems. Nonetheless, these solutions mainly focus on ensuring the controller's effectiveness, overlooking the explainability of the final result. As a step toward explaining the outcome of DeePC for the control of nonlinear systems, in this paper, we focus on analyzing the earliest and simplest DeePC approach proposed to cope with nonlinearities in the controlled system, using a Lasso regularization. Our theoretical analysis highlights that the decisions undertaken by DeePC with Lasso regularization are unexplainable, as control actions are determined by data incoherent with the system's local behavior. This result is true even when the available input/output samples are grouped according to the different operating conditions explored during data collection. Our numerical study confirms these findings, highlighting the benefits of data grouping in terms of performance while showing that explainability remains a challenge in control design via DeePC.

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arXiv2025

In-Context Learning for Zero-Shot Speed Estimation of BLDC motors

Accurate speed estimation in sensorless brushless DC motors is essential for high-performance control and monitoring, yet conventional model-based approaches struggle with system nonlinearities and parameter uncertainties. In this work, we propose an in-context learning framework leveraging transformer-based models to perform zero-shot speed estimation using only electrical measurements. By training the filter offline on simulated motor trajectories, we enable real-time inference on unseen real motors without retraining, eliminating the need for explicit system identification while retaining adaptability to varying operating conditions. Experimental results demonstrate that our method outperforms traditional Kalman filter-based estimators, especially in low-speed regimes that are crucial during motor startup.

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arXiv2025

Innovation diffusion dynamics toward long-term behavioral shifts

Sustainable technologies and services can play a pivotal role in the transition to "greener" habits. Their widespread adoption is thus crucial, and understanding how to foster this phenomenon in a systematic way could have a major impact on our future. With this in mind, in this work we propose an extension of the Friedkin-Johnsen opinion dynamics model toward characterizing the long-term impact of (structural) fostering policies. We then propose alternative nudging strategies that target a trade-off between widespread adoption and investments under budget constraints, showing the impact of our modeling and design choices on inclination shifts over a set of numerical tests.

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arXiv2025

Optimal Policy Design for Repeated Decision-Making under Social Influence

In this paper, we present a novel model to characterize individual tendencies in repeated decision-making scenarios, with the goal of designing model-based control strategies that promote virtuous choices amidst social and external influences. Our approach builds on the classical Friedkin and Johnsen model of social influence, extending it to include random factors (e.g., inherent variability in individual needs) and controllable external inputs. We explicitly account for the temporal separation between two processes that shape opinion dynamics: individual decision-making and social imitation. While individual decisions occur at regular, frequent intervals, the influence of social imitation unfolds over longer periods. The inclusion of random factors naturally leads to dynamics that do not converge in the classical sense. However, under specific conditions, we prove that opinions exhibit ergodic behavior. Building on this result, we propose a constrained asymptotic optimal control problem designed to foster, on average, social acceptance of a target action within a network. To address the transient dynamics of opinions, we reformulate this problem within a Model Predictive Control (MPC) framework. Simulations highlight the significance of accounting for these transient effects in steering individuals toward virtuous choices while managing policy costs.

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arXiv2025

Optimal policy design for decision problems under social influence

This paper focuses on describing the impact of policy actions on individuals' opinions in the presence of social and external influences toward proposing preliminary nudging strategies to achieve a cost-effectiveness trade-off. To this end, we extend the classical Friedkin and Johnsen model of opinion dynamics to incorporate random factors, such as variability in individual predispositions due to uncontrolled events (e.g., modeling the impact of the weather on daily mobility choices), and describe the impact of personalized policies. Furthermore, we formulate an optimal control problem aimed at fostering the social acceptance of particular actions/choices within the network. Through our analysis and numerical simulations, we illustrate the features of the proposed model in the absence of nudging and the effectiveness of the proposed (optimal) nudging strategies.

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arXiv2025

Harnessing Uncertainty for a Separation Principle in Direct Data-Driven Predictive Control

Model Predictive Control (MPC) is a powerful method for complex system regulation, but its reliance on an accurate model poses many limitations in real-world applications. Data-driven predictive control (DDPC) aims at overcoming this limitation, by relying on historical data to provide information on the plant to be controlled. In this work, we present a unified stochastic framework for direct DDPC, where control actions are obtained by optimizing the Final Control Error (FCE), which is directly computed from available data only and automatically weighs the impact of uncertainty on the control objective. Our framework allows us to establish a separation principle for Predictive Control, elucidating the role that predictive models and their uncertainty play in DDPC. Moreover, it generalizes existing DDPC methods, like regularized Data-enabled Predictive Control (DeePC) and $γ$-DDPC, providing a path toward noise-tolerant data-based control with rigorous optimality guarantees. The theoretical investigation is complemented by a series of experiments (code available on GitHub: https://github.com/marcofabris92/a-separation-principle-in-d3pc), revealing that the proposed method consistently outperforms or, at worst, matches existing techniques without requiring tuning regularization parameters as other methods do.

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arXiv2024

One controller to rule them all

Imagine having a system to control and only know that it belongs to a certain class of dynamical systems. Would it not be amazing to simply plug in a controller and have it work as intended? With the rise of in-context learning and powerful architectures like Transformers, this might be possible, and we want to show it. In this work, within the model reference framework, we hence propose the first in-context learning-based approach to design a unique contextual controller for an entire class of dynamical systems rather than focusing on just a single instance. Our promising numerical results show the possible advantages of the proposed paradigm, paving the way for a shift from the "one-system-one-controller" control design paradigm to a new "one-class-one-controller" logic.

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arXiv2024

Bias correction and instrumental variables for direct data-driven model-reference control

Managing noisy data is a central challenge in direct data-driven control design. We propose an approach for synthesizing model-reference controllers for linear time-invariant (LTI) systems using noisy state-input data, employing novel noise mitigation techniques. Specifically, we demonstrate that using data-based covariance parameterization of the controller enables bias-correction and instrumental variable techniques within the data-driven optimization, thus reducing measurement noise effects as data volume increases. The number of decision variables remains independent of dataset size, making this method scalable to large datasets. The approach's effectiveness is demonstrated with a numerical example.

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arXiv2024

On the equivalence of direct and indirect data-driven predictive control approaches

Recently, several direct Data-Driven Predictive Control (DDPC) methods have been proposed, advocating the possibility of designing predictive controllers from historical input-output trajectories without the need to identify a model. In this work, we show that these approaches are equivalent to an indirect approach. Reformulating the direct methods in terms of estimated parameters and covariance matrices allows us to give new insights into how they work in comparison with, for example, Subspace Predictive Control (SPC). In particular, we show that for unconstrained problems the direct methods are equivalent to SPC with a reduced weight on the tracking cost. Via a numerical experiment, motivated by the reformulation, we also illustrate why the performance of direct DDPC methods with fixed regularization tends to degrade as the number of training samples increases.

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arXiv2024

Data-driven control of input saturated systems: a LMI-based approach

This paper addresses three complex control challenges related to input-saturated systems from a data-driven perspective. Unlike the traditional two-stage process involving system identification and model-based control, the proposed approach eliminates the need for an explicit model description. The method combines data-based closed-loop representations, Lyapunov theory, instrumental variables, and a generalized sector condition to formulate data-driven linear matrix inequalities (LMIs). These LMIs are applied to maximize the origin's basin of attraction, minimize the closed-loop reachable set with bounded disturbances, and introduce a new data-driven $\ell_2$-gain minimization problem. Demonstrations on benchmark examples highlight the advantages and limitations of the proposed approach compared to an explicit identification of the system, emphasizing notable benefits in handling nonlinear dynamics.

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arXiv2024

Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees

In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature.

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arXiv2024

On the impact of regularization in data-driven predictive control

Model predictive control (MPC) is a control strategy widely used in industrial applications. However, its implementation typically requires a mathematical model of the system being controlled, which can be a time-consuming and expensive task. Data-driven predictive control (DDPC) methods offer an alternative approach that does not require an explicit mathematical model, but instead optimize the control policy directly from data. In this paper, we study the impact of two different regularization penalties on the closed-loop performance of a recently introduced data-driven method called $γ$-DDPC. Moreover, we discuss the tuning of the related coefficients in different data and noise scenarios, to provide some guidelines for the end user.

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arXiv2024

Meta-learning of data-driven controllers with automatic model reference tuning: theory and experimental case study

Data-driven control offers a viable option for control scenarios where constructing a system model is expensive or time-consuming. Nonetheless, many of these algorithms are not entirely automated, often necessitating the adjustment of multiple hyperparameters through cumbersome trial-and-error processes and demanding significant amounts of data. In this paper, we explore a meta-learning approach to leverage potentially existing prior knowledge about analogous (though not identical) systems, aiming to reduce both the experimental workload and ease the tuning of the available degrees of freedom. We validate this methodology through an experimental case study involving the tuning of proportional, integral (PI) controllers for brushless DC (BLDC) motors with variable loads and architectures.

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arXiv2024

SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study

In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.

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arXiv2024

Explainable data-driven modeling via mixture of experts: towards effective blending of grey and black-box models

Traditional models grounded in first principles often struggle with accuracy as the system's complexity increases. Conversely, machine learning approaches, while powerful, face challenges in interpretability and in handling physical constraints. Efforts to combine these models often often stumble upon difficulties in finding a balance between accuracy and complexity. To address these issues, we propose a comprehensive framework based on a "mixture of experts" rationale. This approach enables the data-based fusion of diverse local models, leveraging the full potential of first-principle-based priors. Our solution allows independent training of experts, drawing on techniques from both machine learning and system identification, and it supports both collaborative and competitive learning paradigms. To enhance interpretability, we penalize abrupt variations in the expert's combination. Experimental results validate the effectiveness of our approach in producing an interpretable combination of models closely resembling the target phenomena.

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arXiv2023

Fair-MPC: a control-oriented framework for socially just decision-making

Control theory can play a pivotal role in tackling many of the global challenges currently affecting our society, representing an actionable tool to help policymakers in shaping our future. At the same time, for this to be possible, elements of social justice must be accounted for within a control theoretical framework, so as not to exacerbate the existing divide in our society. In turn, this requires the formulation of new constraints and control objectives and their integration into existing or new control design strategies. Devising a formally sound framework to ensure social fairness can enable a leap in the comprehension of the meaning of such goals and their non-trivial relation with the usual notion of performance in control. In this new and challenging context, we propose Fair-MPC, an economic model predictive control scheme to promote fairness in control design and model-based decision-making. Moving beyond traditional measures of performance, Fair-MPC enables the integration of social fairness metrics, articulated in equality and equity, allowing the design of optimal input sequences to trade-off fairness and efficiency, which are often in conflict. By establishing a theoretical link between Fair-MPC and the standard model predictive control framework (quadratic cost and linear constraints), we provide insights into the impact of social justice objectives on the final control action, which is ultimately assessed along the efficiency of the controller over two numerical examples.

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arXiv2023

In-context learning of state estimators

State estimation has a pivotal role in several applications, including but not limited to advanced control design. Especially when dealing with nonlinear systems state estimation is a nontrivial task, often entailing approximations and challenging fine-tuning phases. In this work, we propose to overcome these challenges by formulating an in-context state-estimation problem, enabling us to learn a state estimator for a class of (nonlinear) systems abstracting from particular instances of the state seen during training. To this end, we extend an in-context learning framework recently proposed for system identification, showing via a benchmark numerical example that this approach allows us to (i) use training data directly for the design of the state estimator, (ii) not requiring extensive fine-tuning procedures, while (iii) achieving superior performance compared to state-of-the-art benchmarks.

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arXiv2023

Meta-learning for model-reference data-driven control

One-shot direct model-reference control design techniques, like the Virtual Reference Feedback Tuning (VRFT) approach, offer time-saving solutions for the calibration of fixed-structure controllers for dynamic systems. Nonetheless, such methods are known to be highly sensitive to the quality of the available data, often requiring long and costly experiments to attain acceptable closed-loop performance. These features might prevent the widespread adoption of such techniques, especially in low-data regimes. In this paper, we argue that the inherent similarity of many industrially relevant systems may come at hand, offering additional information from plants that are similar (yet not equal) to the system one aims to control. Assuming that this supplementary information is available, we propose a novel, direct design approach that leverages the data from similar plants, the knowledge of controllers calibrated on them, and the corresponding closed-loop performance to enhance model-reference control design. More specifically, by constructing the new controller as a combination of the available ones, our approach exploits all the available priors following a meta-learning philosophy, while ensuring non-decreasing performance. An extensive numerical analysis supports our claims, highlighting the effectiveness of the proposed method in achieving performance comparable to iterative approaches, while at the same time retaining the efficiency of one-shot direct data-driven methods like VRFT.

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