Related papers: Finding, Stabilizing, and Verifying Cycles of Nonl…
This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that…
Group synchronization plays a crucial role in global pipelines for Structure from Motion (SfM). Its formulation is nonconvex and it is faced with highly corrupted measurements. Cycle consistency has been effective in addressing these…
Increasingly demanding performance requirements for dynamical systems motivates the adoption of nonlinear and adaptive control techniques. One challenge is the nonlinearity of the resulting closed-loop system complicates verification that…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall…
This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
In this paper we study the stabilization problem of a general class of slow-fast systems with one fast and arbitrarily many slow states. Moreover, the class of systems under study is slowly actuated, meaning that only the slow states are…
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
The controllability problem for nonlinear control systems with one-dimensional control of the form $ dx/dt=a(x)+B(x)\beta(x,u)$ is considered, where $a(x)$ is an $n$-dimensional vector function, $B(x)$ is an $(n\times m)$-matrix, and…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type principle is proposed…
Cyclic reduction is a method for the solution of (block-)tridiagonal linear systems. In this note we review the method tailored to hermitian positive definite banded linear systems. The reviewed method has the following advantages: It is…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
Neural networks have demonstrated remarkable success in modeling nonlinear dynamical systems. However, identifying these systems from closed-loop experimental data remains a challenge due to the correlations induced by the feedback loop.…
For a discrete dynamical system on $\R$ generated by a quadratic function, we show, using elementary computations, that the existence, number, and stability of 3-cycles are determined by a single parameter depending on the coefficients of…