arXiv subjects

Alessandro Chiuso

Publications and source records attributed to Alessandro Chiuso.

At least 19 recordsLinked to original sources

arXiv2025

Grid-Connected, Data-Driven Inverter Control, Theory to Hardware

Grid-connected inverter control is challenging to implement due to the difficulty of obtaining and maintaining an accurate grid model. Direct Data-Driven Predictive Control provides a model-free alternative to traditional model-based control methods. This paper describes how the recently-proposed Transient Predictive Control (TPC) can be used for real-world, plug-and-play inverter control. The following hypotheses were tested: 1) The TPC algorithm can be run online using standard hardware, and 2) TPC, which is derived using Linear Time-Invariant assumptions, is effective for grid-connected inverter control, which is a nonlinear and time-varying system. Experiments conducted on a two-converter benchtop setup and at the CoSES Laboratory on a 25 kVA converter connected to the Munich grid support these hypotheses.

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arXiv2025

The Bias of Subspace-based Data-Driven Predictive Control

This paper quantifies and addresses the bias of subspace-based Data-Driven Predictive Control (DDPC) for linear, time-invariant (LTI) systems. The primary focus is the bias that arises when the training data is gathered with a feedback controller in closed-loop with the system. First, the closed-loop bias of Subspace Predictive Control is quantified using the training data innovations. Next, the bias of direct, subspace-based DDPC methods DeePC and $\gamma$-DDPC is shown to consist of two parts--the Subspace Bias, which arises from closed-loop data, and an Optimism Bias, which arises from DeePC/$\gamma$-DDPC's "optimistic" adjustment of the output trajectory. We show that, unlike subspace-based DDPC methods, Transient Predictive Control does not suffer from Subspace Bias or Optimism Bias. Double integrator experiments demonstrate that Subspace and Optimism Bias are responsible for poor reference tracking by the subspace-based DDPC methods.

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arXiv2025

Policy Gradient Adaptive Control for the LQR: Indirect and Direct Approaches

Motivated by recent advances of reinforcement learning and direct data-driven control, we propose policy gradient adaptive control (PGAC) for the linear quadratic regulator (LQR), which uses online closed-loop data to improve the control policy while maintaining stability. Our method adaptively updates the policy in feedback by descending the gradient of the LQR cost and is categorized as indirect, when gradients are computed via an estimated model, versus direct, when gradients are derived from data using sample covariance parameterization. Beyond the vanilla gradient, we also showcase the merits of the natural gradient and Gauss-Newton methods for the policy update. Notably, natural gradient descent bridges the indirect and direct PGAC, and the Gauss-Newton method of the indirect PGAC leads to an adaptive version of the celebrated Hewer's algorithm. To account for the uncertainty from noise, we propose a regularization method for both indirect and direct PGAC. For all the considered PGAC approaches, we show closed-loop stability and convergence of the policy to the optimal LQR gain. Simulations validate our theoretical findings and demonstrate the robustness and computational efficiency of PGAC.

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arXiv2025

Regularization for Covariance Parameterization of Direct Data-Driven LQR Control

As the benchmark of data-driven control methods, the linear quadratic regulator (LQR) problem has gained significant attention. A growing trend is direct LQR design, which finds the optimal LQR gain directly from raw data and bypassing system identification. To achieve this, our previous work develops a direct LQR formulation parameterized by sample covariance. In this paper, we propose a regularization method for the covariance-parameterized LQR. We show that the regularizer accounts for the uncertainty in both the steady-state covariance matrix corresponding to closed-loop stability, and the LQR cost function corresponding to averaged control performance. With a positive or negative coefficient, the regularizer can be interpreted as promoting either exploitation or exploration, which are well-known trade-offs in reinforcement learning. In simulations, we observe that our covariance-parameterized LQR with regularization can significantly outperform the certainty-equivalence LQR in terms of both the optimality gap and the robust closed-loop stability.

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arXiv2024

Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQR

Direct data-driven design methods for the linear quadratic regulator (LQR) mainly use offline or episodic data batches, and their online adaptation has been acknowledged as an open problem. In this paper, we propose a direct adaptive method to learn the LQR from online closed-loop data. First, we propose a new policy parameterization based on the sample covariance to formulate a direct data-driven LQR problem, which is shown to be equivalent to the certainty-equivalence LQR with optimal non-asymptotic guarantees. Second, we design a novel data-enabled policy optimization (DeePO) method to directly update the policy, where the gradient is explicitly computed using only a batch of persistently exciting (PE) data. Third, we establish its global convergence via a projected gradient dominance property. Importantly, we efficiently use DeePO to adaptively learn the LQR by performing only one-step projected gradient descent per sample of the closed-loop system, which also leads to an explicit recursive update of the policy. Under PE inputs and for bounded noise, we show that the average regret of the LQR cost is upper-bounded by two terms signifying a sublinear decrease in time $\mathcal{O}(1/\sqrt{T})$ plus a bias scaling inversely with signal-to-noise ratio (SNR), which are independent of the noise statistics. Finally, we perform simulations to validate the theoretical results and demonstrate the computational and sample efficiency of our method.

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arXiv2023

Harnessing Uncertainty for a Separation Principle in Direct Data-Driven Predictive Control

Model Predictive Control (MPC) is a powerful method for complex system regulation, but its reliance on an accurate model poses many limitations in real-world applications. Data-driven predictive control (DDPC) aims at overcoming this limitation, by relying on historical data to provide information on the plant to be controlled. In this work, we present a unified stochastic framework for direct DDPC, where control actions are obtained by optimizing the Final Control Error (FCE), which is directly computed from available data only and automatically weighs the impact of uncertainty on the control objective. Our framework allows us to establish a separation principle for Predictive Control, elucidating the role that predictive models and their uncertainty play in DDPC. Moreover, it generalizes existing DDPC methods, like regularized Data-enabled Predictive Control (DeePC) and $\gamma$-DDPC, providing a path toward noise-tolerant data-based control with rigorous optimality guarantees. The theoretical investigation is complemented by a series of experiments (code available on GitHub: https://github.com/marcofabris92/a-separation-principle-in-d3pc), revealing that the proposed method consistently outperforms or, at worst, matches existing techniques without requiring tuning regularization parameters as other methods do.

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arXiv2023

Dynamic Brain Networks with Prescribed Functional Connectivity

In this paper, we consider stable stochastic linear systems modeling whole-brain resting-state dynamics. We parametrize the state matrix of the system (effective connectivity) in terms of its steady-state covariance matrix (functional connectivity) and a skew-symmetric matrix $S$. We examine how the matrix $S$ influences some relevant dynamic properties of the system. Specifically, we show that a large $S$ enhances the degree of stability and excitability of the system, and makes the latter more responsive to high-frequency inputs.

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arXiv2023

Simulation of Nonlinear Systems Trajectories: between Models and Behaviors

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories. In particular, we focus on equivalent representations of the systems in the two frameworks for the problem of simulating a future nonlinear system trajectory starting from a given set of noisy data. The goal also includes extending some existing results from the deterministic to the stochastic setting.

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arXiv2023

On the impact of regularization in data-driven predictive control

Model predictive control (MPC) is a control strategy widely used in industrial applications. However, its implementation typically requires a mathematical model of the system being controlled, which can be a time-consuming and expensive task. Data-driven predictive control (DDPC) methods offer an alternative approach that does not require an explicit mathematical model, but instead optimize the control policy directly from data. In this paper, we study the impact of two different regularization penalties on the closed-loop performance of a recently introduced data-driven method called $\gamma$-DDPC. Moreover, we discuss the tuning of the related coefficients in different data and noise scenarios, to provide some guidelines for the end user.

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arXiv2022

Uncertainty-aware data-driven predictive control in a stochastic setting

Data-Driven Predictive Control (DDPC) has been recently proposed as an effective alternative to traditional Model Predictive Control (MPC), in that the same constrained optimization problem can be addressed without the need to explicitly identify a full model of the plant. However, DDPC is built upon input/output trajectories. Therefore, the finite sample effect of stochastic data, due to, e.g., measurement noise, may have a detrimental impact on closed-loop performance. Exploiting a formal statistical analysis of the prediction error, in this paper we propose the first systematic approach to deal with uncertainty due to finite sample effects. To this end, we introduce two regularization strategies for which, differently from existing regularization-based DDPC techniques, we propose a tuning rationale allowing us to select the regularization hyper-parameters before closing the loop and without additional experiments. Simulation results confirm the potential of the proposed strategy when closing the loop.

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arXiv2022

Data-driven predictive control in a stochastic setting: a unified framework

Data-driven predictive control (DDPC) has been recently proposed as an effective alternative to traditional model-predictive control (MPC) for its unique features of being time-efficient and unbiased with respect to the oracle solution. Nonetheless, it has also been observed that noise may strongly jeopardize the final closed-loop performance since it affects both the data-based system representation and the control update computed from the online measurements. Recent studies have shown that regularization is potentially a successful tool to counteract the effect of noise. At the same time, regularization requires the tuning of a set of penalty terms, whose choice might be practically difficult without closed-loop experiments. In this paper, by means of subspace identification tools, we pursue a three-fold goal: $(i)$ we set up a unified framework for the existing regularized data-driven predictive control schemes for stochastic systems; $(ii)$ we introduce $\gamma$-DDPC, an efficient two-stage scheme that splits the optimization problem into two parts: fitting the initial conditions and optimizing the future performance, while guaranteeing constraint satisfaction; $(iii)$ we discuss the role of regularization for data-driven predictive control, providing new insight on $when$ and $how$ it should be applied. A benchmark numerical case study finally illustrates the performance of $\gamma$-DDPC, showing how controller design can be simplified in terms of tuning effort and computational complexity when benefiting from the insights coming from the subspace identification realm.

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arXiv2021

A novel Deep Neural Network architecture for non-linear system identification

We present a novel Deep Neural Network (DNN) architecture for non-linear system identification. We foster generalization by constraining DNN representational power. To do so, inspired by fading memory systems, we introduce inductive bias (on the architecture) and regularization (on the loss function). This architecture allows for automatic complexity selection based solely on available data, in this way the number of hyper-parameters that must be chosen by the user is reduced. Exploiting the highly parallelizable DNN framework (based on Stochastic optimization methods) we successfully apply our method to large scale datasets.

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arXiv2021

Estimating Koopman operators for nonlinear dynamical systems: a nonparametric approach

The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most popular finite dimensional approximation. In this paper we capture their core essence as a dual version of the same framework, incorporating them into the Kernel framework. To do so, we leverage the RKHS as a suitable space for learning the Koopman dynamics, thanks to its intrinsic finite-dimensional nature, shaped by data. We finally establish a strong link between kernel methods and Koopman operators, leading to the estimation of the latter through Kernel functions. We provide also simulations for comparison with standard procedures.

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arXiv2019

Stable spline identification of linear systems under missing data

A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian framework as zero-mean Gaussian processes. Their covariances are given by the so-called stable spline kernels encoding information on regularity and BIBO stability. In this paper, we demonstrate that these kernels also lead to a new family of radial basis functions kernels suitable to model system components subject to disturbances given by filtered white noise. This novel class, in cooperation with the stable spline kernels, paves the way to a new approach to solve missing data problems in both discrete and continuous-time settings. Numerical experiments show that the new technique may return models more predictive than those obtained by standard parametric Prediction Error Methods, also when these latter exploit the full data set.

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arXiv2018

Derivative-free online learning of inverse dynamics models

This paper discusses online algorithms for inverse dynamics modelling in robotics. Several model classes including rigid body dynamics (RBD) models, data-driven models and semiparametric models (which are a combination of the previous two classes) are placed in a common framework. While model classes used in the literature typically exploit joint velocities and accelerations, which need to be approximated resorting to numerical differentiation schemes, in this paper a new `derivative-free' framework is proposed that does not require this preprocessing step. An extensive experimental study with real data from the right arm of the iCub robot is presented, comparing different model classes and estimation procedures, showing that the proposed `derivative-free' methods outperform existing methodologies.

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arXiv2018

The role of noise modeling in the estimation of resting-state brain effective connectivity

Causal relations among neuronal populations of the brain are studied through the so-called effective connectivity (EC) network. The latter is estimated from EEG or fMRI measurements, by inverting a generative model of the corresponding data. It is clear that the goodness of the estimated network heavily depends on the underlying modeling assumptions. In this present paper we consider the EC estimation problem using fMRI data in resting-state condition. Specifically, we investigate on how to model endogenous fluctuations driving the neuronal activity.

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arXiv2017

Estimating effective connectivity in linear brain network models

Contemporary neuroscience has embraced network science to study the complex and self-organized structure of the human brain; one of the main outstanding issues is that of inferring from measure data, chiefly functional Magnetic Resonance Imaging (fMRI), the so-called effective connectivity in brain networks, that is the existing interactions among neuronal populations. This inverse problem is complicated by the fact that the BOLD (Blood Oxygenation Level Dependent) signal measured by fMRI represent a dynamic and nonlinear transformation (the hemodynamic response) of neuronal activity. In this paper, we consider resting state (rs) fMRI data; building upon a linear population model of the BOLD signal and a stochastic linear DCM model, the model parameters are estimated through an EM-type iterative procedure, which alternately estimates the neuronal activity by means of the Rauch-Tung-Striebel (RTS) smoother, updates the connections among neuronal states and refines the parameters of the hemodynamic model; sparsity in the interconnection structure is favoured using an iteratively reweighting scheme. Experimental results using rs-fMRI data are shown demonstrating the effectiveness of our approach and comparison with state of the art routines (SPM12 toolbox) is provided.

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arXiv2017

The Harmonic Analysis of Kernel Functions

Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian process with zero mean and with a certain kernel (i.e. covariance) function. Choosing the kernel is one of the most challenging and important issues. In the present paper we introduce the harmonic analysis of this non-stationary process, and argue that this is an important tool which helps in designing such kernel. Furthermore, this analysis suggests also an effective way to approximate the kernel, which allows to reduce the computational burden of the identification procedure.

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