arXiv subjects

Fabio Pasqualetti

Publications and source records attributed to Fabio Pasqualetti.

At least 37 records · Page 2Linked to original sources

arXiv2025

Global Optimization Through Heterogeneous Oscillator Ising Machines

Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a promising computing paradigm for solving complex optimization problems that are intractable on existing digital computers. However, their performance is sensitive to the choice of tunable parameters, and convergence guarantees are mostly lacking. Here, we show that lower energy states are more likely to be stable, and that convergence to the global minimizer is often improved by introducing random heterogeneities in the regularization parameters. Our analysis relates the stability properties of Ising configurations to the spectral properties of a signed graph Laplacian. By examining the spectra of random ensembles of these graphs, we show that the probability of an equilibrium being asymptotically stable depends inversely on the value of the Ising Hamiltonian, biasing the system toward low-energy states. Our numerical results confirm our findings and demonstrate that heterogeneously designed OIMs efficiently converge to globally optimal solutions with high probability.

math.OC↗

arXiv2025

Transfer Learning for LQR Control

In this paper, we study a transfer learning framework for Linear Quadratic Regulator (LQR) control, where (i) the dynamics of the system of interest (target system) are unknown and only a short trajectory of impulse responses from the target system is provided, and (ii) impulse responses are available from $N$ source systems with different dynamics. We show that the LQR controller can be learned from a sufficiently long trajectory of impulse responses. Further, a transferable mode set can be identified using the available data from source systems and the target system, enabling the reconstruction of the target system's impulse responses for controller design. By leveraging data from source systems, we show that the sample complexity for synthesizing the LQR controller can be reduced by $50 \%$. Algorithms and numerical examples are provided to demonstrate the implementation of the proposed transfer control framework.

eess.SY↗

arXiv2025

Oscillatory Associative Memory with Exponential Capacity

The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular interest is the challenge of incorporating memory efficiently into the learning process. Inspired by how human brains store and retrieve information, associative memory mechanisms provide a class of computational methods that can store and retrieve patterns in a robust, energy-efficient manner. Existing associative memory architectures, such as the celebrated Hopfield model and oscillatory associative memory networks, store patterns as stable equilibria of network dynamics. However, the capacity (i.e. the number of patterns that a network can memorize normalized by their number of nodes) of existing oscillatory models have been shown to decrease with the size of the network, making them impractical for large-scale, real-world applications. In this paper, we propose a novel associative memory architecture based on Kuramoto oscillators. We show that the capacity of our associative memory network increases exponentially with network size and features no spurious memories. In addition, we present algorithms and numerical experiments to support these theoretical findings, providing guidelines for the hardware implementation of the proposed associative memory networks.

eess.SY↗

arXiv2025

Online Optimization with Unknown Time-varying Parameters

In this paper, we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools to identify the dynamics of the parameters, predict their evolution, and ultimately compute a solution to the optimization problem. The identification of the dynamics of the time-varying parameters is done online using measurements of the gradient of the cost function. This system identification problem is not standard, since the output matrix is known and the dynamics of the parameters must be estimated in the original coordinates without similarity transformations. Interestingly, our analysis shows that, under mild conditions that we characterize, the identification of the parameters dynamics and, consequently, the computation of a time-varying solution to the optimization problem, requires only a finite number of measurements of the gradient of the cost function. We illustrate the effectiveness of our algorithm on a series of numerical examples.

math.OC↗

arXiv2025

Charge-Density-Wave Oscillator Networks for Solving Combinatorial Optimization Problems

Many combinatorial optimization problems fall into the non-polynomial time NP-hard complexity class, characterized by computational demands that increase exponentially with the size of the problem in the worst case. Solving large-scale combinatorial optimization problems efficiently requires novel hardware solutions beyond the conventional von Neumann architecture. We propose an approach for solving a type of NP-hard problem based on coupled oscillator networks implemented with charge-density-wave condensate devices. Our prototype hardware, based on the 1T polymorph of TaS2, reveals the switching between the charge-density-wave electron-phonon condensate phases, enabling room-temperature operation of the network. The oscillator operation relies on hysteresis in current-voltage characteristics and bistability triggered by applied electrical bias. This work presents a network of injection-locked, coupled oscillators whose phase dynamics follow the Kuramoto model and demonstrates that such coupled quantum oscillators naturally evolve to a ground state capable of solving combinatorial optimization problems. The coupled oscillators based on charge-density-wave condensate phases can efficiently solve NP-hard Max-Cut benchmark problems, offering advantages over other leading oscillator-based approaches. The nature of the transitions between the charge-density-wave phases, distinctively different from resistive switching, creates the potential for low-power operation and compatibility with conventional Si technology.

cond-mat.mtrl-sci↗

arXiv2025

Controllable Neural Architectures for Multi-Task Control

This paper studies a multi-task control problem where multiple linear systems are to be regulated by a single non-linear controller. In particular, motivated by recent advances in multi-task learning and the design of brain-inspired architectures, we consider a neural controller with (smooth) ReLU activation function. The parameters of the controller are a connectivity matrix and a bias vector: although both parameters can be designed, the connectivity matrix is constant while the bias vector can be varied and is used to adapt the controller across different control tasks. The bias vector determines the equilibrium of the neural controller and, consequently, of its linearized dynamics. Our multi-task control strategy consists of designing the connectivity matrix and a set of bias vectors in a way that the linearized dynamics of the neural controller for the different bias vectors provide a good approximation of a set of desired controllers. We show that, by properly choosing the bias vector, the linearized dynamics of the neural controller can replicate the dynamics of any single, linear controller. Further, we design gradient-based algorithms to train the parameters of the neural controller, and we provide upper and lower bounds for the performance of our neural controller. Finally, we validate our results using different numerical examples.

eess.SY↗

arXiv2024

Predicting AI Agent Behavior through Approximation of the Perron-Frobenius Operator

Predicting the behavior of AI-driven agents is particularly challenging without a preexisting model. In our paper, we address this by treating AI agents as nonlinear dynamical systems and adopting a probabilistic perspective to predict their statistical behavior using the Perron-Frobenius (PF) operator. We formulate the approximation of the PF operator as an entropy minimization problem, which can be solved by leveraging the Markovian property of the operator and decomposing its spectrum. Our data-driven methodology simultaneously approximates the PF operator to perform prediction of the evolution of the agents and also predicts the terminal probability density of AI agents, such as robotic systems and generative models. We demonstrate the effectiveness of our prediction model through extensive experiments on practical systems driven by AI algorithms.

cs.AI↗

arXiv2024

Analytical Characterization of Epileptic Dynamics in a Bistable System

Epilepsy is one of the most common neurological disorders globally, affecting millions of individuals. Despite significant advancements, the precise mechanisms underlying this condition remain largely unknown, making accurately predicting and preventing epileptic seizures challenging. In this paper, we employ a bistable model, where a stable equilibrium and a stable limit cycle coexist, to describe epileptic dynamics. The equilibrium captures normal steady-state neural activity, while the stable limit cycle signifies seizure-like oscillations. The noise-driven switch from the equilibrium to the limit cycle characterizes the onset of seizures. The differences in the regions of attraction of these two stable states distinguish epileptic brain dynamics from healthy ones. We analytically construct the regions of attraction for both states. Further, using the notion of input-to-state stability, we theoretically show how the regions of attraction influence the stability of the system subject to external perturbations. Generalizing the bistable system into coupled networks, we also find the role of network parameters in shaping the regions of attraction. Our findings shed light on the intricate interplay between brain networks and epileptic activity, offering mechanistic insights into potential avenues for more predictable treatments.

eess.SY↗

arXiv2024

Denoising Diffusion-Based Control of Nonlinear Systems

We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that have achieved success in a wide variety of sampling tasks. In our framework, we pose the feedback control problem as a generative task of drawing samples from a target set under control system constraints. The forward process of DDPMs constructs trajectories originating from a target set by adding noise. We learn to control a dynamical system in reverse such that the terminal state belongs to the target set. For control-affine systems without drift, we prove that the control system can exactly track the trajectory of the forward process in reverse, whenever the the Lie bracket based condition for controllability holds. We numerically study our approach on various nonlinear systems and verify our theoretical results. We also conduct numerical experiments for cases beyond our theoretical results on a physics-engine.

math.OC↗

arXiv2023

Navigation Systems May Deteriorate Stability in Traffic Networks

Advanced traffic navigation systems, which provide routing recommendations to drivers based on real-time congestion information, are nowadays widely adopted by roadway transportation users. Yet, the emerging effects on the traffic dynamics originating from the widespread adoption of these tools have remained largely unexplored until now. In this paper, we propose a dynamic model where drivers imitate the path preferences of previous drivers, and we study the properties of its equilibrium points. Our model is a dynamic generalization of the classical traffic assignment framework, and extends it by accounting for dynamics both in the path decision process and in the network's traffic flows. We show that when travelers learn shortest paths by imitating other travelers, the overall traffic system benefits from this mechanism and transfers the maximum admissible amount of traffic demand. On the other hand, we demonstrate that when the travel delay functions are not sufficiently steep or the rates at which drivers imitate previous travelers are not adequately chosen, the trajectories of the traffic system may fail to converge to an equilibrium point, thus failing asymptotic stability. Illustrative numerical simulations combined with empirical data from highway sensors illustrate our findings.

math.OC↗

arXiv2023

Noise in the reverse process improves the approximation capabilities of diffusion models

In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon, comparing neural ordinary differential equations (ODEs) and neural stochastic differential equations (SDEs) as reverse processes. We use a control theoretic perspective by posing the approximation of the reverse process as a trajectory tracking problem. We analyze the ability of neural SDEs to approximate trajectories of the Fokker-Planck equation, revealing the advantages of stochasticity. First, neural SDEs exhibit a powerful regularizing effect, enabling $L^2$ norm trajectory approximation surpassing the Wasserstein metric approximation achieved by neural ODEs under similar conditions, even when the reference vector field or score function is not Lipschitz. Applying this result, we establish the class of distributions that can be sampled using score matching in SGMs, relaxing the Lipschitz requirement on the gradient of the data distribution in existing literature. Second, we show that this approximation property is preserved when network width is limited to the input dimension of the network. In this limited width case, the weights act as control inputs, framing our analysis as a controllability problem for neural SDEs in probability density space. This sheds light on how noise helps to steer the system towards the desired solution and illuminates the empirical success of stochasticity in generative modeling.

cs.LG↗

arXiv2023

Fusing Multiple Algorithms for Heterogeneous Online Learning

This study addresses the challenge of online learning in contexts where agents accumulate disparate data, face resource constraints, and use different local algorithms. This paper introduces the Switched Online Learning Algorithm (SOLA), designed to solve the heterogeneous online learning problem by amalgamating updates from diverse agents through a dynamic switching mechanism contingent upon their respective performance and available resources. We theoretically analyze the design of the selecting mechanism to ensure that the regret of SOLA is bounded. Our findings show that the number of changes in selection needs to be bounded by a parameter dependent on the performance of the different local algorithms. Additionally, two test cases are presented to emphasize the effectiveness of SOLA, first on an online linear regression problem and then on an online classification problem with the MNIST dataset.

cs.LG↗

arXiv2023

Astrocytes as a mechanism for meta-plasticity and contextually-guided network function

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes may play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably versus dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results indicate how the presence of neuron-astrocyte interaction in the brain may benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.

q-bio.NC↗

arXiv2023

Data-Driven Feedback Linearization using the Koopman Generator

This paper contributes a theoretical framework for data-driven feedback linearization of nonlinear control-affine systems. We unify the traditional geometric perspective on feedback linearization with an operator-theoretic perspective involving the Koopman operator. We first show that if the distribution of the control vector field and its repeated Lie brackets with the drift vector field is involutive, then there exists an output and a feedback control law for which the Koopman generator is finite-dimensional and locally nilpotent. We use this connection to propose a data-driven algorithm Koopman Generator-based Feedback Linearization (KGFL) for feedback linearization. Particularly, we use experimental data to identify the state transformation and control feedback from a dictionary of functions for which feedback linearization is achieved in a least-squares sense. We also propose a single-step data-driven formula which can be used to compute the linearizing transformations. When the system is feedback linearizable and the chosen dictionary is complete, our data-driven algorithm provides the same solution as model-based feedback linearization. Finally, we provide numerical examples for the data-driven algorithm and compare it with model-based feedback linearization. We also numerically study the effect of the richness of the dictionary and the size of the data set on the effectiveness of feedback linearization.

math.OC↗

arXiv2023

On the Sample Complexity of the Linear Quadratic Gaussian Regulator

In this paper we provide direct data-driven expressions for the Linear Quadratic Regulator (LQR), the Kalman filter, and the Linear Quadratic Gaussian (LQG) controller using a finite dataset of noisy input, state, and output trajectories. We show that our data-driven expressions are consistent, since they converge as the number of experimental trajectories increases, we characterize their convergence rate, and quantify their error as a function of the system and data properties. These results complement the body of literature on data-driven control and finite-sample analysis, and provide new ways to solve canonical control and estimation problems that do not assume, nor require the estimation of, a model of the system and noise and do not rely on solving implicit equations.

math.OC↗

arXiv2023

Multi-Task System Identification of Similar Linear Time-Invariant Dynamical Systems

This paper presents a system identification framework -- inspired by multi-task learning -- to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems. In particular, we consider LTI systems that model networked systems with similar connectivity, or LTI systems with small differences in their matrices. The system identification task involves the minimization of the least-squares (LS) fit for individual systems, augmented with a regularization function that enforces structural similarities. The proposed method is particularly suitable for cases when the recorded trajectories for one or more LTI systems are not sufficiently rich, leading to ill-conditioning of LS methods. We analyze the performance of the proposed method when the matrices of the LTI systems feature a common sparsity pattern (i.e., similar connectivity), and provide simulations based on real data for the estimation of the brain dynamics. We show that the proposed method requires a significantly smaller number of fMRI scans to achieve similar error levels of the LS.

eess.SY↗

arXiv2023

Vibrational Stabilization of Cluster Synchronization in Oscillator Networks

Cluster synchronization is of paramount importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as neurological disorders in the brain. Therefore, it is crucial to restore normal system functions by stabilizing the appropriate cluster synchronization patterns. Most existing studies focus on designing controllers based on state measurements to achieve system stabilization. However, in many real-world scenarios, measuring system states, such as neuronal activity in the brain, poses significant challenges, rendering the stabilization of such systems difficult. To overcome this challenge, in this paper, we employ an open-loop control strategy, vibrational control, which does not requires any state measurements. We establish some sufficient conditions under which vibrational inputs stabilize cluster synchronization. Further, we provide a tractable approach to design vibrational control. Finally, numerical experiments are conducted to demonstrate our theoretical findings.

math.OC↗

arXiv2023

Imitation and Transfer Learning for LQG Control

In this paper we study an imitation and transfer learning setting for Linear Quadratic Gaussian (LQG) control, where (i) the system dynamics, noise statistics and cost function are unknown and expert data is provided (that is, sequences of optimal inputs and outputs) to learn the LQG controller, and (ii) multiple control tasks are performed for the same system but with different LQG costs. We show that the LQG controller can be learned from a set of expert trajectories of length $n(l+2)-1$, with $n$ and $l$ the dimension of the system state and output, respectively. Further, the controller can be decomposed as the product of an estimation matrix, which depends only on the system dynamics, and a control matrix, which depends on the LQG cost. This data-based separation principle allows us to transfer the estimation matrix across different LQG tasks, and to reduce the length of the expert trajectories needed to learn the LQG controller to~$2n+m-1$ with $m$ the dimension of the inputs (for single-input systems with $l=2$, this yields approximately a $50\%$ reduction of the required expert data).

eess.SY↗