Related papers: Sequentially learning regions of attraction from d…
We present a one-parameter family of continuous, piecewise affine, area preserving maps of the square, which are inspired by a dynamical system in game theory. Interested in the coexistence of stochastic and (quasi-)periodic behaviour, we…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
We study gradient descent for rank-1 matrix factorization through a certificate-based viewpoint. The central object is a parameterized quadratic certificate $I(\delta;\,\cdot)$ whose level sets shrink along the dynamics, thereby inducing a…
In this paper, we consider the problem of computing estimates of the domain-of-attraction for non-polynomial systems. A polynomial approximation technique, based on multivariate polynomial interpolation and error analysis for remaining…
The paper is concerned with the development of Lyapunov methods for the analysis of equilibrium stability in a dynamical system on the space of probability measures driven by a non-local continuity equation. We derive sufficient conditions…
Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…
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…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
Appropriate estimation of Region of Attraction for a nonlinear dynamical system plays a key role in system analysis and control design. Sum-of-Squares optimization is a powerful tool enabling Region of Attraction estimation for polynomial…
System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as…
We present a new method for learning control law that stabilizes an unknown nonlinear dynamical system at an equilibrium point. We formulate a system identification task in a self-supervised learning setting that jointly learns a controller…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
Continuous piecewise affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
Proper states' representations are the key to the successful dynamics modeling of chaotic systems. Inspired by recent advances of deep representations in various areas such as natural language processing and computer vision, we propose the…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…