arXiv subjects

Giancarlo Ferrari-Trecate

Publications and source records attributed to Giancarlo Ferrari-Trecate.

At least 19 recordsLinked to original sources

arXiv2026

An Accelerated Proximal Gradient Method for Bures-Wasserstein Space

We study composite optimization over the Bures--Wasserstein (BW) space of Gaussian measures. Our main observation is that a useful class of BW problems can be lifted into the Euclidean space of affine transport maps, such that the lifted problems can be solved efficiently using accelerated proximal gradient methods. For objectives whose smooth and nonsmooth components admit convex smooth and convex proximable affine lifts, respectively, our algorithm BW-FISTA achieves minimax-optimal objective gap $O(k^{-2})$ after $k$ iterations. We verify these regularity conditions for potential and interaction energies together with common spectral regularizers, and we treat stochastic gradients under a suitable noise model. As a principal application, we consider Gaussian variational inference with a log-concave, log-smooth target. Here, the resulting entropy term is handled by an efficient, exact proximal step, and we improve the previous rate of $O(k^{-1})$ to $O(k^{-2})$. We numerically verify this predicted boost with synthetic experiments.

math.OC↗

arXiv2026

Neural Closed-Loop Identification of Nonlinear Systems with Stability and Generalization Guarantees

Neural networks are expressive models of nonlinear dynamics, but identifying such systems from closed-loop data raises two difficulties: the feedback loop correlates inputs with measurement noise, biasing standard open-loop estimators, and the identified model must be stabilized by the data-collection controller, so that its closed-loop behavior matches the true plant's. We derive a complete parameterization of all nonlinear systems stabilized by a given controller, generalizing the classical dual-Youla parameterization to the nonlinear setting. Building on this characterization, we propose Internal Controller Identification (ICI), a computationally tractable framework for identifying potentially unstable systems while ensuring closed-loop stability by construction; in the linear case, our indirect method reduces to an open-loop identification problem, for which standard consistency results apply. The framework accommodates contextual information, letting a single certified model identify a family of systems, and supports a PAC-Bayesian training objective that, when data are scarce and prior knowledge is available, bounds the identified operator's expected prediction loss. Experiments show that ICI identifies open-loop unstable plants where uncertified baselines diverge, outperforms direct methods under weak excitation and feedback-correlated noise, generalizes zero-shot to environments unseen during training, and, with limited data, avoids the overfitting of empirical risk minimization while providing a non-vacuous generalization bound.

eess.SY↗

arXiv2026

Distributed Performance Boosting through Neural Control for Plug-and-Play Networks

We address the problem of improving the performance of pre-stabilized networked systems subject to plug-and-play (PnP) operations, namely additions or removals of subsystems. While distributed baseline controllers can preserve stability after a PnP transition, augmenting them with expressive neural policies can invalidate the formal stability guarantees. To overcome this issue, we build on recently proposed Performance Boosting controllers based on the Internal Model Control (IMC) principle, which reduce closed-loop stability to a finite $\ell_2$-gain requirement on an auxiliary operator. In the distributed setting, this operator is formed by interconnecting local neural operators that exchange information only between neighboring subsystems. We then derive free parametrizations of this interconnection, namely explicit maps from unconstrained trainable variables to interconnected neural operators satisfying a prescribed network gain bound for every parameter value. The obtained distributed neural controller can therefore be trained by unconstrained gradient-based optimization without stability constraints or projection steps, while retaining the prescribed gain bound at every training iterate. We develop two complementary parametrizations. A neighbor-based compositional parametrization uses local coupling bounds, so that after a PnP event only subsystems whose bounds change need to update their gain parameters. A network-norm parametrization instead uses a bound on the overall coupling matrix and can reduce conservatism, at the price of requiring network-wide information. A PnP DC-microgrid case study shows that the proposed neural layer improves voltage transients under topology changes and load variations while preserving nominal closed-loop stability.

eess.SY↗

arXiv2026

Differentiable Hybrid-Action Neural Feedback Control for District Heating Networks

Many cyber-physical systems require control policies that combine continuous setpoints with discrete operational de- cisions, such as equipment switching, mode selection, or resource scheduling. Discrete actions are not differentiable, which ob- structs gradient-based policy training, while conventional mixed- integer formulations remain costly to solve online. This paper proposes a hybrid-action neural controller (HANC) in which a continuous branch, a categorical branch and a differentiable assembly layer jointly generate commands that satisfy complex actuator constraints by construction. Categorical decisions are handled using a straight-through Gumbel estimator, enabling the policy to be trained by backpropagation through time over full closed-loop rollouts. The proposed framework is deployed on a district heating network (DHN) featuring multiple heat generation units and stratified thermal energy storage. Its performance is evaluated on a simulation of a real DHN located at RSE SpA in Italy. The resulting policy jointly learns switching decisions and continu- ous operating setpoints. Under dynamic electricity pricing, the learned controller reduces operating cost by 30% compared to a rule-based industrial baseline. We also show that, compared with a deterministic straight-through relaxation, injecting noise during training achieves similar cost while reducing hard switching by an order of magnitude, and attribute this difference to the wider decision margins of the resulting policy.

eess.SY↗

arXiv2026

Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise

We study finite-horizon distributionally robust linear-quadratic control with disturbances that can be arbitrarily correlated in time. The ambiguity set is modeled as a single 2-Wasserstein ball centered at a nominal elliptically contoured distribution of the disturbances. Despite the infinite-dimensionality of both the policy space and ambiguity set, we prove that the optimal policy is affine and that the worst-case distribution is an affine push-forward of the nominal distribution. These affine maps can be computed efficiently via a best-response algorithm based on the Frank--Wolfe algorithm. Experiments demonstrate improved out-of-sample performance over LQG and its distributionally robust extensions when the true disturbances are correlated, incurring only a small loss of performance under uncorrelated disturbances.

math.OC↗

arXiv2026

Context-Enriched Performance Boosting via Operator Decomposition

Performance Boosting (PB) is a control framework that, for a pre-stabilized system subject to $\mathcal L_p$ process disturbances, parametrizes the controllers that preserve closed-loop $\mathcal L_p$-stability through a causal $\mathcal L_p$-stable operator mapping reconstructed disturbances to corrective control actions. Although this permits optimization over expressive stability-preserving controllers, learning a desired policy from disturbance information alone can be difficult. We introduce a structured factorization for context-enriched, multi-input PB operators. The proposed architecture combines an $\mathcal L_p$-stable dynamical module that processes reconstructed disturbances with a uniformly bounded matrix-valued mixer depending on disturbances and contextual signals. Under the standard PB assumptions, this factorization preserves closed-loop $\mathcal L_p$-stability by construction. Moreover, on a weighted-envelope disturbance domain, we prove that the factorization is necessary and sufficient for causal operators satisfying a context-uniform envelope-preservation property. A numerical moving-gate navigation experiment demonstrates the advantages of the proposed architecture over context-agnostic PB, MAD, and reference-aware PB baselines.

eess.SY↗

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.

eess.SY↗

arXiv2026

A graph-informed regret metric for optimal distributed control

We consider the optimal control of large-scale systems using distributed controllers whose network topology mirrors the coupling graph between subsystems. In this work, we introduce spatial regret, a graph-informed metric measuring the worst-case performance gap between a distributed controller and an oracle with access to additional sensor information. The oracle's graph is a user-specified augmentation of the information graph, yielding a benchmark policy that penalizes disturbances for which additional sensing would improve performance. Minimizing spatial regret yields distributed controllers - respecting the nominal information graph - that emulate the oracle's response to disturbances characteristic of large-scale networks, such as localized perturbations. We show that minimizing spatial regret admits a convex reformulation as an infinite program with a finite-dimensional approximation. To scale to large networks, we derive an upper bound on the spatial regret that can be efficiently minimized in a distributed way. Numerical experiments on power-system models show that the resulting controllers mitigate localized disturbances more effectively than those based on classical metrics.

eess.SY↗

arXiv2026

Free Parametrization of L_2-Bounded Structured State-Space Controllers for Nonlinear Control with Stability Guarantees

Designing stabilizing control policies for nonlinear systems while optimizing complex objectives remains a formidable challenge. Neural networks (NNs), despite their expressive power, can be highly sensitive to small input perturbations and can easily destabilize the closed-loop system. Existing approaches often impose explicit constraints on the controller's parameters to ensure stability, but this typically leads to additional computational overhead. To address this issue, we leverage recently proposed structured state-space models (SSMs) to parametrize discrete-time control policies for nonlinear systems. Our key contribution is a new free parametrization of linear time-invariant (LTI) systems with a prescribed L2 gain. We use this result to construct the L2-Recurrent Unit (L2RU), an SSM layer that enforces the desired L2 bound by design. The resulting architecture can be used to guarantee closed-loop stability via the small-gain theorem or the so-called performance-boosting framework, independently of the controller's optimization parameters, thereby enabling fully unconstrained optimization of general nonlinear objectives. Furthermore, the structure induced by the proposed parametrization enables the efficient processing of long input sequences, as it is highly parallelizable through algorithms such as parallel scan. We demonstrate the effectiveness of this approach on a formation-control task for mobile robots, where the L2RU-based controller ensures collision and obstacle avoidance while maintaining stability and performance.

eess.SY↗

arXiv2026

Sinkhorn Ambiguity Sets for Distributionally Robust Control: Convexity, Weak Compactness, and Tractability

Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC) problem with ambiguity sets defined via the Sinkhorn discrepancy. Compared to other discrepancy measures based on optimal transport, such as the popular Wasserstein distance, the Sinkhorn divergence does not constrain the worst-case distribution to be discrete, and allows combining observed data with prior knowledge in the form of a reference distribution, making this choice particularly suitable when only few noise samples are available for control design. We first study the properties of Sinkhorn ambiguity sets, establishing convexity and weak compactness under standard assumptions. We then leverage these results to prove that, the Sinkhorn DR linear quadratic control problem over linear policies can be solved through convex programming-even in the presence of DR safety constraints. Finally, we validate our theoretical findings and demonstrate the effectiveness of the proposed approach on a trajectory planning example.

eess.SY↗

arXiv2026

Data-Driven Optimal Distributed Controller Synthesis via Spatial Regret

In this paper, we present a novel method for synthesising an optimal distributed spatial regret controller using experimentally obtained frequency-response data. Spatial regret provides a measure of the performance gap between a structured distributed controller and an oracle with enhanced communication topology. We relax assumptions on the communication topology, allowing the oracle to adopt any enhanced structure. While this generalisation requires an iterative solution in place of a single convex program, we provide a tractable algorithm that synthesises optimal controllers from frequency-response data while preserving stability and the desired communication structure. Through numerical examples, we illustrate the better performance of the spatial regret controller compared to classical H2/Hinf designs, underscoring the effectiveness of the proposed methodology.

eess.SY↗

arXiv2026

L2RU: a Structured State Space Model with prescribed L2-bound

Structured state-space models (SSMs) have recently emerged as a powerful architecture at the intersection of machine learning and control, featuring layers composed of discrete-time linear time-invariant (LTI) systems followed by pointwise nonlinearities. These models combine the expressiveness of deep neural networks with the interpretability and inductive bias of dynamical systems, offering strong performance on long-sequence tasks with favorable computational complexity. However, their adoption in applications such as system identification and optimal control remains limited by the difficulty of enforcing stability and robustness in a principled and tractable manner. We introduce L2RU, a class of SSMs endowed with a prescribed $\mathcal{L}_2$-gain bound, guaranteeing input--output stability and robustness for all parameter values. The L2RU architecture is derived from free parametrizations of LTI systems satisfying an $\mathcal{L}_2$ constraint, enabling unconstrained optimization via standard gradient-based methods while preserving rigorous stability guarantees. Specifically, we develop two complementary parametrizations: a non-conservative formulation that provides a complete characterization of square LTI systems with a given $\mathcal{L}_2$-bound, and a conservative formulation that extends the approach to general (possibly non-square) systems while improving computational efficiency through a structured representation of the system matrices. Both parametrizations admit efficient initialization schemes that facilitate training long-memory models. We demonstrate the effectiveness of the proposed framework on a nonlinear system identification benchmark, where L2RU achieves improved performance and training stability compared to existing SSM architectures, highlighting its potential as a principled and robust building block for learning and control.

eess.SY↗

arXiv2026

Controller Design for Structured State-space Models via Contraction Theory

This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling time-series data and dynamical systems. They can capture long-term dependencies while maintaining linear computational complexity with respect to the sequence length, in comparison to the quadratic complexity of Transformer-based architectures. The contributions of this work are threefold. We provide the first analysis of controllability and observability of SSMs, which leads to scalable control design via Linear Matrix Inequalities (LMIs) that leverage contraction theory. Moreover, a separation principle for SSMs is established, enabling the independent design of observers and state-feedback controllers while preserving the exponential stability of the closed-loop system. The effectiveness of the proposed framework is demonstrated through a numerical example, showcasing nonlinear system identification and the synthesis of an output feedback controller.

eess.SY↗

arXiv2026

On the Global Optimality of Linear Policies for Sinkhorn Distributionally Robust Linear Quadratic Control

The Linear Quadratic Gaussian (LQG) regulator is a cornerstone of optimal control theory, yet its performance can degrade significantly when the noise distributions deviate from the assumed Gaussian model. To address this limitation, this work proposes a distributionally robust generalization of the finite-horizon LQG control problem. Specifically, we assume that the noise distributions are unknown and belong to ambiguity sets defined in terms of an entropy-regularized Wasserstein distance centered at a nominal Gaussian distribution. By deriving novel bounds on this Sinkhorn discrepancy and proving structural and topological properties of the resulting ambiguity sets, we establish global optimality of linear policies. Numerical experiments showcase improved distributional robustness of our control policy.

eess.SY↗

arXiv2026

Learning stabilising policies for constrained nonlinear systems

This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional closed-loop l_p-stability of the error in tracking a desired equilibrium and the satisfaction of input and output constraints within a robustly positive invariant set. An additional control contribution, derived by combining the internal model control principle with a stable operator, is introduced to improve system performance. This operator, implemented as a stable neural network, can be trained via unconstrained optimisation on a chosen performance metric, without compromising closed-loop equilibrium tracking or constraint satisfaction, even if the optimisation is stopped prematurely. In addition, we characterise the class of closed-loop stable behaviours that can be achieved with the proposed architecture. Simulation results on a pH-neutralisation benchmark demonstrate the effectiveness of the proposed approach.

eess.SY↗

arXiv2026

Stability-Preserving Online Adaptation of Neural Closed-loop Maps

The growing complexity of modern control tasks calls for controllers that can react online as objectives and disturbances change, while preserving closed-loop stability. Recent approaches for improving the performance of nonlinear systems while preserving closed-loop stability rely on time-invariant recurrent neural-network controllers, but offer no principled way to update the controller during operation. Most importantly, switching from one stabilizing policy to another can itself destabilize the closed-loop. We address this problem by introducing a stability-preserving update mechanism for nonlinear, neural-network-based controllers. Each controller is modeled as a causal operator with bounded $\ell_p$-gain, and we derive gain-based conditions under which the controller may be updated online. These conditions yield two practical update schemes, time-scheduled and state-triggered, that guarantee the closed-loop remains $\ell_p$-stable after any number of updates. Our analysis further shows that stability is decoupled from controller optimality, allowing approximate or early-stopped controller synthesis. We demonstrate the approach on nonlinear systems with time-varying objectives and disturbances, and show consistent performance improvements over static and naive online baselines while guaranteeing stability.

eess.SY↗

arXiv2026

Safety-Aware Performance Boosting for Constrained Nonlinear Systems

We study a control architecture for nonlinear constrained systems that integrates a performance-boosting (PB) controller with a scheduled Predictive Safety Filter (PSF). The PSF acts as a pre-stabilizing base controller that enforces state and input constraints. The PB controller, parameterized as a causal operator, influences the PSF in two ways: it proposes a performance input to be filtered, and it provides a scheduling signal to adjust the filter's Lyapunov-decrease rate. We prove two main results: (i) Stability by design: any controller adhering to this parametrization maintains closed-loop stability of the pre-stabilized system and inherits PSF safety. (ii) Trajectory-set expansion: the architecture strictly expands the set of safe, stable trajectories achievable by controllers combined with conventional PSFs, which rely on a pre-defined Lyapunov decrease rate to ensure stability. This scheduling allows the PB controller to safely execute complex behaviors, such as transient detours, that are provably unattainable by standard PSF formulations. We demonstrate this expanded capability on a constrained inverted pendulum task with a moving obstacle.

eess.SY↗

arXiv2026

Boosting the transient performance of reference tracking controllers with neural networks

Reference tracking is a key objective in many control systems, including those characterized by complex nonlinear dynamics. In these settings, traditional control approaches can effectively ensure steady-state accuracy but often struggle to explicitly optimize transient performance. Neural network controllers have gained popularity due to their adaptability to nonlinearities and disturbances; however, they often lack formal closed-loop stability and performance guarantees. To address these challenges, a recently proposed neural-network control framework known as Performance Boosting (PB) has demonstrated the ability to maintain $\mathcal{L}_p$ stability properties of nonlinear systems while optimizing generic transient costs. This paper extends the PB approach to reference tracking problems. First, we characterize the complete set of nonlinear controllers that preserve desired tracking properties for nonlinear systems equipped with base reference-tracking controllers. Then, we show how to optimize transient costs while searching within subsets of tracking controllers that incorporate expressive neural network models. Furthermore, we analyze the robustness of our method to uncertainties in the underlying system dynamics. Numerical simulations on a robotic system demonstrate the advantages of our approach over the standard PB framework.

eess.SY↗