arXiv subjects

Giancarlo Ferrari-Trecate

Publications and source records attributed to Giancarlo Ferrari-Trecate.

At least 37 records · Page 2Linked to original sources

arXiv2025

Resilient AFE Drive Control using Neural Networks with Tracking Guarantees

Industrial installations across several sectors have seen a dramatic increase in productivity, accuracy and efficiency over the last decade due to expanded utilization of medium voltage, variable speed power electronic converters to drive their processes. Specifically, active front-end (AFE) drives have become popular due to their ability to deliver power while maintaining safe electrical setpoints. However, under abnormal grid conditions such as phase loss, conventional AFE control may fail to enforce safety constraints, potentially leading to drive shutdown and significant financial losses. In this work, we propose using reference-tracking Performance Boosting (rPB) to improve the resilience of standard AFE control to faults. This neural-network control framework provides a principled way to optimize transient performance while preserving the steady-state tracking properties of AFE-based drives. By carefully shaping the input signals to the rPB controller, we ensure that it activates only during grid faults, leaving nominal operation unaffected. Simulation results show that the proposed approach successfully maintains the DC bus voltage and the grid current within safe limits during single-phase loss events.

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arXiv2025

PAC-Bayesian Optimal Control with Stability and Generalization Guarantees

Stochastic Nonlinear Optimal Control (SNOC) seeks to minimize a cost function that accounts for random disturbances acting on a nonlinear dynamical system. Since the expectation over all disturbances is generally intractable, a common surrogate is the empirical cost, obtained by averaging over a finite dataset of sampled noise realizations. This substitution, however, introduces the challenge of guaranteeing performance under unseen disturbances. The issue is particularly severe when the dataset is limited, as the trained controllers may overfit, leading to substantial gaps between their empirical cost and the deployment cost. In this work, we develop a PAC-Bayesian framework that establishes rigorous generalization bounds for SNOC. Building on these bounds, we propose a principled controller design method that balances empirical performance and prior knowledge. To ensure tractability, we derive computationally efficient relaxations of the bounds and employ approximate inference methods. Our framework further leverages expressive neural controller parameterizations, guaranteeing closed-loop stability. Through simulated examples, we highlight how prior knowledge can be incorporated into control design and how more reliable controllers can be synthesized for cooperative robotics.

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arXiv2025

Neural Identification of Feedback-Stabilized Nonlinear Systems

Neural networks have demonstrated remarkable success in modeling nonlinear dynamical systems. However, identifying these systems from closed-loop experimental data remains a challenge due to the correlations induced by the feedback loop. Traditional nonlinear closed-loop system identification methods struggle with reliance on precise noise models, robustness to data variations, or computational feasibility. Additionally, it is essential to ensure that the identified model is stabilized by the same controller used during data collection, ensuring alignment with the true system's closed-loop behavior. The dual Youla parameterization provides a promising solution for linear systems, offering statistical guarantees and closed-loop stability. However, extending this approach to nonlinear systems presents additional complexities. In this work, we propose a computationally tractable framework for identifying complex, potentially unstable systems while ensuring closed-loop stability using a complete parameterization of systems stabilized by a given controller. We establish asymptotic consistency in the linear case and validate our method through numerical comparisons, demonstrating superior accuracy over direct identification baselines and compatibility with the true system in stability properties.

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arXiv2025

MAD: A Magnitude And Direction Policy Parametrization for Stability Constrained Reinforcement Learning

We introduce magnitude and direction (MAD) policies, a policy parameterization for reinforcement learning (RL) that preserves Lp closed-loop stability for nonlinear dynamical systems. Despite their completeness in describing all stabilizing controllers, methods based on nonlinear Youla and system-level synthesis are significantly impacted by the difficulty of parametrizing Lp-stable operators. In contrast, MAD policies introduce explicit feedback on state-dependent features - a key element behind the success of reinforcement learning pipelines - without jeopardizing closed-loop stability. This is achieved by letting the magnitude of the control input be described by a disturbance-feedback Lp-stable operator, while selecting its direction based on state-dependent features through a universal function approximator. We further characterize the robust stability properties of MAD policies under model mismatch. Unlike existing disturbance-feedback policy parametrizations, MAD policies introduce state-feedback components compatible with model-free RL pipelines, ensuring closed-loop stability with no model information beyond assuming open-loop stability. Numerical experiments show that MAD policies trained with deep deterministic policy gradient (DDPG) methods generalize to unseen scenarios - matching the performance of standard neural network policies while guaranteeing closed-loop stability by design.

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arXiv2025

Data-driven Distributionally Robust Control Based on Sinkhorn Ambiguity Sets

As the complexity of modern control systems increases, it becomes challenging to derive an accurate model of the uncertainty that affects their dynamics. Wasserstein Distributionally Robust Optimization (DRO) provides a powerful framework for decision-making under distributional uncertainty only using noise samples. However, while the resulting policies inherit strong probabilistic guarantees when the number of samples is sufficiently high, their performance may significantly degrade when only a few data are available. Inspired by recent results from the machine learning community, we introduce an entropic regularization to penalize deviations from a given reference distribution and study data-driven DR control over Sinkhorn ambiguity sets. We show that for finite-horizon control problems, the optimal DR linear policy can be computed via convex programming. By analyzing the relation between the ambiguity set defined in terms of Wasserstein and Sinkhorn discrepancies, we reveal that, as the regularization parameter increases, this optimal policy interpolates between the solution of the Wasserstein DR problem and that of the stochastic problem under the reference distribution. We validate our theoretical findings and the effectiveness of our approach when only scarce data are available on a numerical example.

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arXiv2025

Robust Convolution Neural ODEs via Contractivity-promoting regularization

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems, and propose to use contraction theory to improve their robustness. For a contractive dynamical system two trajectories starting from different initial conditions converge to each other exponentially fast. Contractive Convolutional NODEs can enjoy increased robustness as slight perturbations of the features do not cause a significant change in the output. Contractivity can be induced during training by using a regularization term involving the Jacobian of the system dynamics. To reduce the computational burden, we show that it can also be promoted using carefully selected weight regularization terms for a class of NODEs with slope-restricted activation functions. The performance of the proposed regularizers is illustrated through benchmark image classification tasks on MNIST and FashionMNIST datasets, where images are corrupted by different kinds of noise and attacks.

cs.LG↗

arXiv2025

Parametrizations of All Stable Closed-loop Responses: From Theory to Neural Network Control Design

The complexity of modern control systems necessitates architectures that achieve high performance while ensuring robust stability, particularly for nonlinear systems. In this work, we tackle the challenge of designing output-feedback controllers to boost the performance of $\ell_p$-stable discrete-time nonlinear systems while preserving closed-loop stability from external disturbances to input and output channels. Leveraging operator theory and neural network representations, we parametrize the achievable closed-loop maps for a given system and propose novel parametrizations of all $\ell_p$-stabilizing controllers, unifying frameworks such as nonlinear Youla parametrization and internal model control. Contributing to a rapidly growing research line, our approach enables unconstrained optimization exclusively over stabilizing controllers and provides sufficient conditions to ensure robustness against model mismatch. Additionally, our methods reveal that stronger notions of stability can be imposed on the closed-loop maps if disturbance realizations are available after one time step. Last, our approaches are compatible with the design of nonlinear distributed controllers. Numerical experiments on cooperative robotics demonstrate the flexibility of the proposed framework, allowing cost functions to be freely designed for achieving complex behaviors while preserving stability.

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arXiv2025

En Route Path-planning for Partially Occupied Vehicles in Ride-pooling Systems

Ride-pooling services, such as UberPool and Lyft Shared Saver, enable a single vehicle to serve multiple customers within one shared trip. Efficient path-planning algorithms are crucial for improving the performance of such systems. For partially occupied vehicles with available capacity, we introduce a novel routing algorithm designed to maximize the likelihood of picking up additional passengers while serving the current passengers to their destination. Unlike traditional methods that group passengers and vehicles based on predefined time windows, our algorithm allows for immediate responses to passenger requests. Our approach optimizes travel time while dynamically considering passenger demand and coordinating with other vehicles. Formulated as an integer linear programming (ILP) problem, our method is computationally efficient and suitable for real-time applications. Simulation results demonstrate that our proposed method can significantly enhance service quality.

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arXiv2025

Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery

Imitation learning is a data-driven approach to learning policies from expert behavior, but it is prone to unreliable outcomes in out-of-sample (OOS) regions. While previous research relying on stable dynamical systems guarantees convergence to a desired state, it often overlooks transient behavior. We propose a framework for learning policies modeled by contractive dynamical systems, ensuring that all policy rollouts converge regardless of perturbations, and in turn, enable efficient OOS recovery. By leveraging recurrent equilibrium networks and coupling layers, the policy structure guarantees contractivity for any parameter choice, which facilitates unconstrained optimization. We also provide theoretical upper bounds for worst-case and expected loss to rigorously establish the reliability of our method in deployment. Empirically, we demonstrate substantial OOS performance improvements for simulated robotic manipulation and navigation tasks.

cs.LG↗

arXiv2025

A PAC-Bayesian Framework for Optimal Control with Stability Guarantees

Stochastic Nonlinear Optimal Control (SNOC) involves minimizing a cost function that averages out the random uncertainties affecting the dynamics of nonlinear systems. For tractability reasons, this problem is typically addressed by minimizing an empirical cost, which represents the average cost across a finite dataset of sampled disturbances. However, this approach raises the challenge of quantifying the control performance against out-of-sample uncertainties. Particularly, in scenarios where the training dataset is small, SNOC policies are prone to overfitting, resulting in significant discrepancies between the empirical cost and the true cost, i.e., the average SNOC cost incurred during control deployment. Therefore, establishing generalization bounds on the true cost is crucial for ensuring reliability in real-world applications. In this paper, we introduce a novel approach that leverages PAC-Bayes theory to provide rigorous generalization bounds for SNOC. Based on these bounds, we propose a new method for designing optimal controllers, offering a principled way to incorporate prior knowledge into the synthesis process, which aids in improving the control policy and mitigating overfitting. Furthermore, by leveraging recent parametrizations of stabilizing controllers for nonlinear systems, our framework inherently ensures closed-loop stability. The effectiveness of our proposed method in incorporating prior knowledge and combating overfitting is shown by designing neural network controllers for tasks in cooperative robotics.

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arXiv2024

Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach

The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing complex costs remains a significant challenge. Neural Networks (NNs), known for their expressivity, can be leveraged to parametrize control policies that yield good performance. However, NNs' sensitivity to small input changes poses a risk of destabilizing the closed-loop system. Many existing approaches enforce constraints on the controllers' parameter space to guarantee closed-loop stability, leading to computationally expensive optimization procedures. To address these problems, we leverage the framework of port-Hamiltonian systems to design continuous-time distributed control policies for nonlinear systems that guarantee closed-loop stability and finite $\mathcal{L}_2$ or incremental $\mathcal{L}_2$ gains, independent of the optimzation parameters of the controllers. This eliminates the need to constrain parameters during optimization, allowing the use of standard techniques such as gradient-based methods. Additionally, we discuss discretization schemes that preserve the dissipation properties of these controllers for implementation on embedded systems. The effectiveness of the proposed distributed controllers is demonstrated through consensus control of non-holonomic mobile robots subject to collision avoidance and averaged voltage regulation with weighted power sharing in DC microgrids.

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arXiv2024

Learning to Boost the Performance of Stable Nonlinear Systems

The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while boosting the performance of nonlinear control systems using data-driven and deep-learning approaches stands as an important unsolved challenge. In this paper, we tackle the performance-boosting problem with closed-loop stability guarantees. Specifically, we establish a synergy between the Internal Model Control (IMC) principle for nonlinear systems and state-of-the-art unconstrained optimization approaches for learning stable dynamics. Our methods enable learning over arbitrarily deep neural network classes of performance-boosting controllers for stable nonlinear systems; crucially, we guarantee L_p closed-loop stability even if optimization is halted prematurely, and even when the ground-truth dynamics are unknown, with vanishing conservatism in the class of stabilizing policies as the model uncertainty is reduced to zero. We discuss the implementation details of the proposed control schemes, including distributed ones, along with the corresponding optimization procedures, demonstrating the potential of freely shaping the cost functions through several numerical experiments.

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arXiv2024

SIMBa: System Identification Methods leveraging Backpropagation

This manuscript details and extends the SIMBa toolbox (System Identification Methods leveraging Backpropagation) presented in previous work, which uses well-established Machine Learning tools for discrete-time linear multi-step-ahead state-space System Identification (SI). SIMBa leverages linear-matrix-inequality-based free parametrizations of Schur matrices to guarantee the stability of the identified model by design. In this paper, backed up by novel free parametrizations of Schur matrices, we extend the toolbox to show how SIMBa can incorporate known sparsity patterns or true values of the state-space matrices to identify without jeopardizing stability. We extensively investigate SIMBa's behavior when identifying diverse systems with various properties from both simulated and real-world data. Overall, we find it consistently outperforms traditional stable subspace identification methods, and sometimes significantly, especially when enforcing desired model properties. These results hint at the potential of SIMBa to pave the way for generic structured nonlinear SI. The toolbox is open-sourced on https://github.com/Cemempamoi/simba.

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arXiv2024

Maximum likelihood inference for high-dimensional problems with multiaffine variable relations

Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very difficult to establish convergence guarantees. This leads to a wide use of brute-force methods, such as grid searching and Monte-Carlo sampling and, when applicable, complex and problem-specific algorithms. In this paper, we consider inference problems where the variables are related by multiaffine expressions. We propose a novel Alternating and Iteratively-Reweighted Least Squares (AIRLS) algorithm, and prove its convergence for problems with Generalized Normal Distributions. We also provide an efficient method to compute the variance of the estimates obtained using AIRLS. Finally, we show how the method can be applied to graphical statistical models. We perform numerical experiments on several inference problems, showing significantly better performance than state-of-the-art approaches in terms of scalability, robustness to noise, and convergence speed due to an empirically observed super-linear convergence rate.

stat.ML↗

arXiv2024

Optimal distributed control with stability guarantees by training a network of neural closed-loop maps

This paper proposes a novel approach to improve the performance of distributed nonlinear control systems while preserving stability by leveraging Deep Neural Networks (DNNs). We build upon the Neural System Level Synthesis (Neur-SLS) framework and introduce a method to parameterize stabilizing control policies that are distributed across a network topology. A distinctive feature is that we iteratively minimize an arbitrary control cost function through an unconstrained optimization algorithm, all while preserving the stability of the overall network architecture by design. This is achieved through two key steps. First, we establish a method to parameterize interconnected Recurrent Equilibrium Networks (RENs) that guarantees a bounded $\mathcal{L}_2$ gain at the network level. This ensures stability. Second, we demonstrate how the information flow within the network is preserved, enabling a fully distributed implementation where each subsystem only communicates with its neighbors. To showcase the effectiveness of our approach, we present a simulation of a distributed formation control problem for a fleet of vehicles. The simulation demonstrates how the proposed neural controller enables the vehicles to maintain a desired formation while navigating obstacles and avoiding collisions, all while guaranteeing network stability.

math.OC↗

arXiv2024

Regret Optimal Control for Uncertain Stochastic Systems

We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant optimal policy that has foreknowledge of both the system dynamics and the exogenous disturbances. In this competitive framework, establishing robustness guarantees proves challenging as, differently from the case where the model is known, the clairvoyant optimal policy is not only inapplicable, but also impossible to compute without knowledge of the system parameters. To address this challenge, we embrace a scenario optimization approach, and we propose minimizing regret robustly over a finite set of randomly sampled system parameters. We prove that this policy optimization problem can be solved through semidefinite programming, and that the corresponding solution retains strong probabilistic out-of-sample regret guarantees in face of the uncertain dynamics. Our method naturally extends to include satisfaction of safety constraints with high probability. We validate our theoretical results and showcase the potential of our approach by means of numerical simulations.

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arXiv2024

Hierarchical Control for Vehicle Repositioning in Autonomous Mobility on Demand Systems

Balancing passenger demand and vehicle availability is crucial for ensuring the sustainability and effectiveness of urban transportation systems. To address this challenge, we propose a novel hierarchical strategy for the efficient distribution of empty vehicles in urban areas. The proposed approach employs a data-enabled predictive control algorithm to develop a high-level controller, which guides the inter-regional allocation of idle vehicles. This algorithm utilizes historical data on passenger demand and vehicle supply in each region to construct a non-parametric representation of the system, enabling it to determine the optimal number of vehicles to be repositioned or retained in their current regions without modeling the system. At the low level, a coverage control-based controller is designed to provide inter-regional position guidance, determining the desired road intersection each vehicle should target. With the objective of optimizing area coverage, it aligns the vehicle distribution with the demand across different districts within a single region. The effectiveness of the proposed method is validated through simulation experiments on the real road network of Shenzhen, China. The integration of the two layers provides better performance compared to applying either layer in isolation, demonstrating its potential to reduce passenger waiting time and answer more requests, thus promoting the development of more efficient and sustainable transportation systems.

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arXiv2024

Safe Zeroth-Order Optimization Using Quadratic Local Approximations

This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging towards a KKT primal-dual pair. Assuming to have prior knowledge on the smoothness of the unknown objective and constraints, we propose a novel zeroth-order method that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. Under some mild assumptions, we prove that this method returns an $η$-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within $O({1}/{η^{2}})$ iterations. Moreover, we numerically show that our method can achieve faster convergence compared with some state-of-the-art zeroth-order approaches. The effectiveness of the proposed approach is also illustrated by applying it to nonconvex optimization problems in optimal control and power system operation.

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