Related papers: Data-driven system analysis of nonlinear systems u…
Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…
In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
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…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result,…
In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems…
In this paper, we will discuss how operational limitations affect input-output behaviours of the system. In particular, we will provide formulations for passivity and passivity indices of a nonlinear system given operational limitations on…
This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
This paper studies data-driven stabilization of a class of unknown polynomial systems using data corrupted by bounded noise. Existing work addressing this problem has focused on designing a controller and a Lyapunov function so that a…
In this paper, we establish an iterative data-driven approach to derive guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In this context, nonlinearity measures quantify the strength of the nonlinearity of a dynamical…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…