Related papers: On Three Generalizations of Contraction
Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…
The paper presents the generalized persistency of excitation conditions. They are not only valid for much broader range of applications than their classical counterparts but also elegantly prove the validity of the latter. The novelty and…
A geometric generalization of contraction theory called~$k$-contraction was recently developed using $k$-compound matrices. In this note, we focus on the relations between $k$-contraction and two other generalized contraction frameworks:…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.
This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…
This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or "nilsequence") behaviour in two different directions…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…
We explicitly carry out the symplectic quantization of a family of multi-field Generalized Proca (GP) electrodynamics theories. In the process, we provide an independent derivation of the so-called secondary constraint enforcing relations…