arXiv subjects

Pietro Tesi

Publications and source records attributed to Pietro Tesi.

At least 19 recordsLinked to original sources

arXiv2026

Machines that Predict Trajectories from Templates

We study trajectory prediction from libraries of stored output templates. Given the past of an unknown trajectory, the goal is to predict its future without identifying the state-space model that generated it. We show that libraries of trajectories generated by one or more dynamical systems define behavioral spaces that can be used as prediction mechanisms. For linear systems, we characterize exact prediction in terms of continuation maps, behavioral containment, and spectral conditions on output-visible eigenvalues. We also analyze robustness to noisy observations and noisy libraries, derive error bounds for out-of-library trajectories, and show how interconnection constraints can compose template libraries into new behavioral spaces with emergent modes. Finally, we extend the framework to nonlinear systems whose output trajectories are contained in, or immersed into, finite-dimensional linear behaviors. These results provide a theory of template-based prediction machines capable of generalizing beyond the stored trajectories and, in some cases, beyond the systems that generated them.

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arXiv2025

Event-triggered control of nonlinear systems from data

In a recent paper [8], we introduced a data-based approach to design event-triggered controllers for linear systems directly from data. Here, we extend the results in [8] to a class of nonlinear systems. We provide two data-based designs certified by a (classical) Lyapunov function. For these two designs, we devise event-triggered policies that rely on the previously found Lyapunov function, have parameters tuned from data, ensure a positive minimum inter-event time, and act based either on the state error or on the library error. These two different policies, and their respective advantages, are illustrated numerically.

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arXiv2024

Data-driven harmonic output regulation of a class of nonlinear systems

The paper deals with the data-based design of state-feedback controllers that solve the output regulation problem for a class of nonlinear systems. Inspired by recent developments in model-based output regulation design techniques and in data-driven control design for nonlinear systems, we derive a data-dependent semidefinite program that, when solved, directly returns a controller that steers the regulation error to a periodic signal whose Fourier series has identically zero coefficients up to a certain order set by the controller. When specialized to the case of linear systems, the result appears to improve upon existing work. Numerical results illustrate the findings

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arXiv2024

A Versatile Framework for Data-Driven Control of Nonlinear Systems

This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the generation of novel results in this domain. We formulate the nonlinear design problem from a high-level perspective as a set of desired controlled systems and propose systematic procedures to synthesize data-driven control algorithms that meet the specified design requirements. Various examples are presented to demonstrate the applicability of the proposed approach and its ability to derive new insights and results, illustrating the novel contributions enabled by the framework.

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arXiv2024

Enforcing contraction via data

We present data-based conditions for enforcing contractivity via feedback control and obtain desired asymptotic properties of the closed-loop system. We focus on unknown nonlinear control systems whose vector fields are expressible via a dictionary of functions and derive data-dependent semidefinite programs whose solution returns the controller that guarantees contractivity. When data are perturbed by disturbances that are linear combinations of sinusoids of known frequencies (but unknown amplitude and phase) and constants, we remarkably obtain conditions for contractivity that do not depend on the magnitude of the disturbances, with imaginable positive consequences for the synthesis of the controller. Finally, we show how to design from data an integral controller for nonlinear systems that achieves constant reference tracking and constant disturbance rejection.

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arXiv2023

Data-based Transfer Stabilization in Linear Systems

We present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the source system, whereas the data from the target system is scarce. We consider both cases where data collected from the source system is noiseless and noisy. For each case, by leveraging the data collected from the source system and a priori knowledge on the maximum distance of the two systems, we find a suitable, and relatively small, compact set of systems that contains the actual target system, and then provide a controller that stabilizes the compact set. In particular, the controller can be obtained by solving a set of linear matrix inequalities (LMIs). Feasibility of those LMIs is discussed in details. We complement our theoretical findings by two numerical case studies of low-order and high-order systems.

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arXiv2023

Data-driven control of nonlinear systems from input-output data

The design of controllers from data for nonlinear systems is a challenging problem. In a recent paper, De Persis, Rotulo and Tesi, "Learning controllers from data via approximate nonlinearity cancellation," IEEE Transactions on Automatic Control, 2023, a method to learn controllers that make the closed-loop system stable and dominantly linear was proposed. The approach leads to a simple solution based on data-dependent semidefinite programs. The method uses input-state measurements as data, while in a realistic setup it is more likely that only input-output measurements are available. In this note we report how the design principle of the above mentioned paper can be adjusted to deal with input-output data and obtain dynamic output feedback controllers in a favourable setting.

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arXiv2023

Data-driven stabilizer design and closed-loop analysis of general nonlinear systems via Taylor's expansion

For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system can be expressed or well-approximated by the basis functions and the experimental data. For a more general setting where explicit information on the basis functions is not available, this paper presents a data-driven approach for stabilizer design and closed-loop analysis via the Lyapunov method. First, based on Taylor's expansion and using input-state data, a stabilizer and a Lyapunov function are designed to render the known equilibrium locally asymptotically stable. Then, data-driven conditions are derived to check whether a given sublevel set of the found Lyapunov function is an invariant subset of the region of attraction. One of the main challenges is how to handle Taylor's remainder in the design of the local stabilizers and the analysis of the closed-loop performance.

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arXiv2023

Learning controllers from data via kernel-based interpolation

We propose a data-driven control design method for nonlinear systems that builds on kernel-based interpolation. Under some assumptions on the system dynamics, kernel-based functions are built from data and a model of the system, along with deterministic model error bounds, is determined. Then, we derive a controller design method that aims at stabilizing the closed-loop system by cancelling out the system nonlinearities. The proposed method can be implemented using semidefinite programming and returns positively invariant sets for the closed-loop system.

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arXiv2022

Event-triggered Control From Data

We present a data-based approach to design event-triggered state-feedback controllers for unknown continuous-time linear systems affected by disturbances. By an event, we mean state measurements transmission from the sensors to the controller over a digital network. By exploiting a sufficiently rich finite set of noisy state measurements and inputs collected off-line, we first design a data-driven state-feedback controller to ensure an input-to-state stability property for the closed-loop system ignoring the network. We then take into account sampling induced by the network and we present robust data-driven triggering strategies to (approximately) preserve this stability property. The approach is general in the sense that it allows deriving data-based versions of various popular triggering rules of the literature. In all cases, the designed transmission policies ensure the existence of a (global) strictly positive minimum inter-event times thereby excluding Zeno phenomenon despite disturbances. These results can be viewed as a step towards plug-and-play control for networked control systems, i.e., mechanisms that automatically learn to control and to communicate over a network.

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arXiv2022

Topology identification of autonomous quantum dynamical networks

Topology identification comprises reconstructing the interaction Hamiltonian of a quantum network by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology contexts, ranging from quantum communication to quantum computing or sensing. In this paper, we provide analytical conditions for the solvability of the topology identification problem for autonomous quantum dynamical networks. The solvability condition is then converted in an algorithm for quantum network reconstruction that is easily implementable on standard computer facilities. The obtained algorithm is tested for Hamiltonian reconstruction on numerical examples based on the quantum walks formalism.

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arXiv2022

Learning Controllers from Data via Approximate Nonlinearity Cancellation

We introduce a method to deal with the data-driven control design of nonlinear systems. We derive conditions to design controllers via (approximate) nonlinearity cancellation. These conditions take the compact form of data-dependent semi-definite programs. The method returns controllers that can be certified to stabilize the system even when data are perturbed and disturbances affect the dynamics of the system during the execution of the control task, in which case an estimate of the robustly positively invariant set is provided.

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arXiv2021

Data-driven design of safe control for polynomial systems

We consider the problem of designing an invariant set using only a finite set of input-state data collected from an unknown polynomial system in continuous time. We consider noisy data, i.e., corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces invariance of a set and also optimizes the size of the invariant set while keeping it within a set of user-defined safety constraints; the solution of this program directly provides a polynomial invariant set and a state-feedback controller. We numerically test the design on a system of two platooning cars.

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arXiv2021

Learning controllers for performance through LMI regions

In an open-loop experiment, an input sequence is applied to an unknown linear time-invariant system (in continuous or discrete time) affected also by an unknown-but-bounded disturbance sequence (with an energy or instantaneous bound); the corresponding state sequence is measured. The goal is to design directly from the input and state sequences a controller that enforces a certain performance specification on the transient behaviour of the unknown system. The performance specification is expressed through a subset of the complex plane where closed-loop eigenvalues need to belong, a so called LMI region. For this control design problem, we provide here convex programs to enforce the performance specification from data in the form of linear matrix inequalities (LMI). For generic LMI regions, these are sufficient conditions to assign the eigenvalues within the LMI region for all possible dynamics consistent with data, and become necessary and sufficient conditions for special LMI regions. In this way, we extend classical model-based conditions from a seminal work in the literature to the setting of data-driven control from noisy data. Through two numerical examples, we investigate how these data-based conditions compare with each other.

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arXiv2021

Direct data-driven model-reference control with Lyapunov stability guarantees

In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block, which are shaped from data to reproduce the desired behavior in closed-loop. By focusing on the case where the reference model and the plant share the same order, we propose an optimal design procedure with Lyapunov stability guarantees, tailored to handle state measurements with additive noise. Two simulation examples are finally illustrated to show the potential of the proposed strategy as compared to the state of the art approaches.

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arXiv2021

Data-driven control via Petersen's lemma

We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an open-loop experiment. In the presence of noise in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen's lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen's lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through (convex) sum-of-squares programs. The findings are illustrated numerically.

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arXiv2021

On the Certainty-Equivalence Approach to Direct Data-Driven LQR Design

The linear quadratic regulator (LQR) problem is a cornerstone of automatic control, and it has been widely studied in the data-driven setting. The various data-driven approaches can be classified as indirect (i.e., based on an identified model) versus direct or as robust (i.e., taking uncertainty into account) versus certainty-equivalence. Here we show how to bridge these different formulations and propose a novel, direct, and regularized formulation. We start from indirect certainty-equivalence LQR, i.e., least-square identification of state-space matrices followed by a nominal model-based design, formalized as a bi-level program. We show how to transform this problem into a single-level, regularized, and direct data-driven control formulation, where the regularizer accounts for the least-square data fitting criterion. For this novel formulation we carry out a robustness and performance analysis in presence of noisy data. Our proposed direct and regularized formulation is also amenable to be further blended with a robust-stability-promoting regularizer. In a numerical case study we compare regularizers promoting either robustness or certainty-equivalence, and we demonstrate the remarkable performance when blending both of them.

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arXiv2021

Online learning of data-driven controllers for unknown switched linear systems

Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under unknown switching signals. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees stability of the closed-loop switched linear system provided that the switching is slow enough. Effectiveness of the proposed design technique is illustrated for two aerospace applications.

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