arXiv subjects

Gianluca Giacomelli

Publications and source records attributed to Gianluca Giacomelli.

4 recordsLinked to original sources

arXiv2026

When Persistency is not Exciting in Data-Driven Predictive Control

Understanding how to collect data that is "meaningful" for control purposes is of paramount importance in data-driven control. While existing approaches have primarily relied on the satisfaction of a rank condition to assess the quality of an experiment, we show that satisfying it is not always sufficient to achieve satisfactory closed-loop performance. Focusing on scenarios where white-noise-like excitation cannot be used for data collection, we examine the frequency-domain implications of linear behavioral representation. This analysis demonstrates that leakage effects are the main driver for data to represent the dynamics of the system. These findings are reflected in our numerical results. Data-enabled predictive controllers built on datasets with insufficient bandwidth, despite fulfilling standard rank conditions, suffer from severe ill-conditioning and fail to achieve reference tracking.

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arXiv2026

Constrained Performance Boosting Control for Nonlinear Systems

We present the Alternating Direction Method of Multipliers (ADMM) for Performance Boosting (PB), an approach for designing neural controllers for stable nonlinear systems subject to state and input constraints. The method builds on an internal model control formulation of PB. In this setting, the controller is parametrized as a stable neural operator, so closed-loop stability is guaranteed by construction, and its weights are trained offline to improve performance. To provide a systematic procedure for promoting constraint satisfaction during training, we reformulate the finite-horizon problem of the PB formulation by introducing auxiliary state and input trajectories. This augmentation allows us to cast an ADMM-based algorithm that alternates between two steps: a gradient-descent-based update of the controller parameters, having the same structure as the PB training problem without explicit constraints, and a projection step that promotes the trajectory feasibility. As a result, this procedure handles constraints during training without altering the controller architecture or compromising its stability-by-design guarantees. Indeed, the stability guarantee follows from the chosen stable controller parametrization, which is not changed in our framework with respect to the foundational PB formulation, and is independent of ADMM convergence. At the same time, this closed-loop stability guarantee does not imply performance optimality or closed-loop constraint satisfaction, which depend on the convergence of ADMM-PB, which is not yet guaranteed in this work. Our numerical results show that, compared with a baseline based on barrier-inspired soft penalties in the loss, ADMM-PB achieves lower constraint violations, at the price of more conservative closed-loop behavior.

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arXiv2026

Beyond Shrinkage: Foundations of Data-Driven Control for Piecewise Affine Systems

Data-enabled predictive control (DeePC) has recently attracted attention as a promising approach for controlling systems directly from raw data, without requiring an explicit identification step. However, DeePC has not yet been extended to piecewise affine (PWA) systems, despite their extensive use in the (predictive) control literature and their universal approximation capabilities. To address this gap, in this work, we lay the foundations for data-enabled predictive control of PWA systems, providing: $(i)$ their behavioral characterization; $(ii)$ an extension of Willems' Fundamental Lemma to represent their behavior from raw data; $(iii)$ an analysis of the coherence of DeePC strategies using a linear predictor and shrinkage regularizers; and $(iv)$ a study of the impact of misclassification errors on structuring data for prediction. Our theoretical findings are validated by numerical results on a simple example, emphasizing the need to extend beyond a regularized version of the foundational DeePC framework to design control actions that are both effective and coherent with a PWA system's behavior, thus ensuring the controller's explainability.

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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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