Alberto Padoan

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Padoan

First Name

Alberto

ORCID

0000-0003-1597-0395

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Publications 1 - 10 of 12

Gaussian behaviors: representations and data-driven control
Sasfi, András; Markovsky, Ivan; Padoan, Alberto; et al. (2025)
We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. The proposed model naturally quantifies the uncertainty in the trajectories, yet it is simple enough to allow for tractable formulations. We relate the proposed model to existing descriptions of dynamical systems including deterministic and stochastic behaviors, and linear time-invariant (LTI) state-space models with Gaussian noise. Gaussian behaviors can be estimated directly from observed data as the empirical sample covariance. The distribution of future outputs conditioned on inputs and past outputs provides a predictive model that can be incorporated in predictive control frameworks. We show that subspace predictive control is a certainty-equivalence control formulation with the estimated Gaussian behavior. Furthermore, the regularized data-enabled predictive control (DeePC) method is shown to be a distributionally optimistic formulation that optimistically accounts for uncertainty in the Gaussian behavior. To mitigate the excessive optimism of DeePC, we propose a novel distributionally robust control formulation, and provide a convex reformulation allowing for efficient implementation.
Behavioral uncertainty quantification for data-driven control
Padoan, Alberto; Coulson, Jeremy; Van Waarde, Henk J.; et al. (2022)
2022 IEEE 61st Conference on Decision and Control (CDC)
This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems’ fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.
How to Represent and Identify Affine Time-Invariant Systems?
Markovsky, Ivan; Eising, Jaap; Padoan, Alberto (2025)
IEEE Control Systems Letters
Affine systems are ubiquitous in modeling and emerge naturally from the linearization of nonlinear dynamics. Despite their relevance in applications, their identification remains largely ad hoc, relying on centering the data before applying linear identification methods. This heuristic approach assumes constant offset and can introduce bias. We develop a dedicated framework for affine system identification, deriving identifiability conditions and identification methods based on difference equation representations. Unlike the classical two-step approach, our method identifies the data-generating system under conditions verifiable from data and system complexity. For noisy data in the errors-in-variables setting, we recast the problem as a structured low-rank approximation, leveraging existing optimization techniques for efficient computation.
Data-driven representations of conical, convex, and affine behaviors
Padoan, Alberto; Dörfler, Florian; Lygeros, John (2023)
2023 62nd IEEE Conference on Decision and Control (CDC)
The paper studies conical, convex, and affine models in the framework of behavioral systems theory. We investigate basic properties of such behaviors and address the problem of constructing models from measured data. We prove that closed, shift-invariant, conical, convex, and affine models have the intersection property, thereby enabling the definition of most powerful unfalsified models based on infinite-horizon measurements. We then provide necessary and sufficient conditions for representing conical, convex, and affine finite-horizon behaviors using raw data matrices, expressing persistence of excitation requirements in terms of non-negative rank conditions. The applicability of our results is demonstrated by a numerical example arising in population ecology.
Model Reduction by Least Squares Moment Matching for Linear and Nonlinear Systems
Padoan, Alberto (2023)
IEEE Transactions on Automatic Control
The paper studies the model reduction problem using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation conditions imposed by moment matching are satisfied in a least squares sense. The paper revisits this idea using tools from output regulation theory to develop a nonlinear enhancement of the notion of least squares moment matching and a unifying model reduction framework both for linear and nonlinear systems. The proposed framework allows for the direct computation of models through optimization, the use of weights to modulate the quality of approximation, and the possibility of enforcing prescribed properties, such as stability and passivity, via additional constraints. Parameterized families of models achieving least squares moment matching are also determined and shown to admit natural geometric and system-theoretic interpretations. The theory is illustrated by numerical examples.
Urban Traffic Congestion Control: A DeePC Change
Rimoldi, Alessio; Cenedese, Carlo; Padoan, Alberto; et al. (2024)
2024 European Control Conference (ECC)
Urban traffic congestion remains a pressing chal-lenge in our rapidly expanding cities, despite the abundance of available data and the efforts of policymakers. By leveraging behavioral system theory and data-driven control, this paper exploits the Data-enabled Predictive Control (DeePC) algorithm in the context of urban traffic control performed via dynamic traffic lights. To validate our approach, we consider a high-fidelity case study using the state-of-the-art simulation software package Simulation of Urban MObility (SUMO). Preliminary results indicate that DeePC outperforms existing approaches across various key metrics, including travel time and CO 2 emissions, demonstrating its potential for effective traffic management.
A quantitative and constructive proof of Willems' Fundamental Lemma and its implications
Berberich, Julian; Iannelli, Andrea; Padoan, Alberto; et al. (2023)
2023 American Control Conference (ACC)
Willems' Fundamental Lemma provides a powerful data-driven parametrization of all trajectories of a controllable linear time-invariant system based on one trajectory with persistently exciting (PE) input. In this paper, we present a novel proof of this result which is inspired by the classical adaptive control literature and differs from existing proofs in multiple aspects. The proof involves a quantitative and directional PE notion, allowing to characterize robust PE properties via singular value bounds, as opposed to binary rank-based PE conditions. Further, the proof is constructive, i.e., we derive an explicit PE lower bound for the generated data. As a contribution of independent interest, we generalize existing PE results from the adaptive control literature and reveal a crucial role of the system's zeros.
Controller implementability: a data-driven approach
Padoan, Alberto; Dörfler, Florian; Coulson, Jeremy (2023)
2023 62nd IEEE Conference on Decision and Control (CDC)
We study the controller implementability problem, which seeks to determine if a controller can make the closed-loop behavior of a given plant match that of a desired reference behavior. We establish necessary and sufficient conditions for controller implementability which only rely on raw data. Subsequently, we consider the problem of constructing controllers directly from data. By leveraging the concept of canonical controller, we provide a formula to directly construct controllers that implement plant-compatible reference behaviors using measurements of both reference and plant behaviors.
Circuit Model Reduction with Scaled Relative Graphs
Chaffey, Thomas; Padoan, Alberto (2022)
2022 IEEE 61st Conference on Decision and Control (CDC)
Continued fractions are classical representations of complex objects (for example, real numbers) as sums and inverses of simpler objects (for example, integers). The analogy in linear circuit theory is a chain of series/parallel one-ports: the port behavior is a continued fraction containing the port behaviors of its elements. Truncating a continued fraction is a classical method of approximation, which corresponds to deleting the circuit elements furthest from the port. We apply this idea to chains of series/parallel one-ports composed of arbitrary nonlinear relations. This gives a model reduction method which automatically preserves properties such as incremental positivity. The Scaled Relative Graph (SRG) gives a graphical representation of the original and truncated port behaviors. The difference of these SRGs gives a bound on the approximation error, which is shown to be competitive with existing methods.
DeePC-Hunt: Data-enabled predictive control hyperparameter tuning via differentiable optimization
Cummins, Michael; Padoan, Alberto; Moffat, Keith; et al. (2025)
Proceedings of Machine Learning Research ~ Proceedings of the 7th Annual Learning for Dynamics & Control Conference
This paper introduces Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimization (DeePC-Hunt), a backpropagation-based method for automatic hyperparameter tuning of the DeePC algorithm. The necessity for such a method arises from the importance of hyperparameter selection to achieve satisfactory closed-loop DeePC performance. The standard methods for hyperparameter selection are to either optimize the open-loop performance, or use manual guess-and-check. Optimizing the open-loop performance can result in unacceptable closed-loop behavior, while manual guess-and-check can pose safety challenges. DeePC-Hunt provides an alternative method for hyperparameter tuning which uses an approximate model of the system dynamics and backpropagation to directly optimize hyperparameters for the closed-loop DeePC performance. Numerical simulations demonstrate the effectiveness of DeePC in combination with DeePC-Hunt in a complex stabilization task for a nonlinear system and its superiority over model-based control strategies in terms of robustness to model misspecifications.

Publications 1 - 10 of 12

Alberto Padoan

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