Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion: Homoclinic orbits, and self-excited and hidden …
In this paper, we discuss self-excited and hidden attractors for systems of differential
equations. We considered the example of a Lorenz-like system derived from the well-known …
equations. We considered the example of a Lorenz-like system derived from the well-known …
Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous
(ie, time-varying) nonlinear system under a contraction metric defined with a uniformly …
(ie, time-varying) nonlinear system under a contraction metric defined with a uniformly …
[HTML][HTML] Review on computational methods for Lyapunov functions
P Giesl, S Hafstein - Discrete and Continuous Dynamical Systems …, 2015 - aimsciences.org
Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both
in theory and applications. They provide sufficient conditions for the stability of equilibria or …
in theory and applications. They provide sufficient conditions for the stability of equilibria or …
On the convergence of stochastic gradient MCMC algorithms with high-order integrators
Recent advances in Bayesian learning with large-scale data have witnessed emergence of
stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin …
stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin …
Decentralized high-performance control of DC microgrids
Direct current (dc) microgrids have been widely used in many critical applications. Such
systems avoid unnecessary ac/dc conversions and can simplify control design. To achieve …
systems avoid unnecessary ac/dc conversions and can simplify control design. To achieve …
Neural contraction metrics for robust estimation and control: A convex optimization approach
H Tsukamoto, SJ Chung - IEEE Control Systems Letters, 2020 - ieeexplore.ieee.org
This letter presents a new deep learning-based framework for robust nonlinear estimation
and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep …
and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep …
Physics-informed neural network Lyapunov functions: PDE characterization, learning, and verification
We provide a systematic investigation of using physics-informed neural networks to compute
Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) …
Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) …
Computing Lyapunov functions using deep neural networks
L Grüne - arXiv preprint arXiv:2005.08965, 2020 - arxiv.org
We propose a deep neural network architecture and a training algorithm for computing
approximate Lyapunov functions of systems of nonlinear ordinary differential equations …
approximate Lyapunov functions of systems of nonlinear ordinary differential equations …
Providing a basin of attraction to a target region of polynomial systems by computation of Lyapunov-like functions
S Ratschan, Z She - SIAM Journal on Control and Optimization, 2010 - SIAM
In this paper, we present a method for computing a basin of attraction to a target region for
polynomial ordinary differential equations. This basin of attraction is ensured by a Lyapunov …
polynomial ordinary differential equations. This basin of attraction is ensured by a Lyapunov …
[图书][B] Random differential equations in scientific computing
This chapter provides a friendly review of the central concepts of probability theory focusing
on random variables and their properties that eventually lead to the notion of a stochastic …
on random variables and their properties that eventually lead to the notion of a stochastic …