相关论文: Review on contraction analysis and computation of …
Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions…
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…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
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 analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
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…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…
The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
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…
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the…
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. The…
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 studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…
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…
The general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…