اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدContinuation of Probability Density Functions using a Generalized Lyapunov Approach
161
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.
قيم البحث
اقرأ أيضاً
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning commutation with rotation, continu
ation beyond the domain of univalence, and periodicity.
We consider the uniqueness of solution (i.e., nonsingularity) of systems of $r$ generalized Sylvester and $star$-Sylvester equations with $ntimes n$ coefficients. After several reductions, we show that it is sufficient to analyze periodic systems hav
ing, at most, one generalized $star$-Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition, and leads to a backward stable $O(n^3r)$ algorithm for computing the (unique) solution.
The multilinear Pagerank model [Gleich, Lim and Yu, 2015] is a tensor-based generalization of the Pagerank model. Its computation requires solving a system of polynomial equations that contains a parameter $alpha in [0,1)$. For $alpha approx 1$, this
computation remains a challenging problem, especially since the solution may be non-unique. Extrapolation strategies that start from smaller values of $alpha$ and `follow the solution by slowly increasing this parameter have been suggested; however, there are known cases where these strategies fail, because a globally continuous solution curve cannot be defined as a function of $alpha$. In this paper, we improve on this idea, by employing a predictor-corrector continuation algorithm based on a more general representation of the solutions as a curve in $mathbb{R}^{n+1}$. We prove several global properties of this curve that ensure the good behavior of the algorithm, and we show in our numerical experiments that this method is significantly more reliable than the existing alternatives.
In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem associated to the
transport problem. We exploit the viewpoint of Wasserstein Hamiltonian flow with initial and target densities, and our method is designed to retain the underlying Hamiltonian structure. Several numerical examples are presented to illustrate the performance of the method.
Stochastic uncertainties in complex dynamical systems lead to variability of system states, which can in turn degrade the closed-loop performance. This paper presents a stochastic model predictive control approach for a class of nonlinear systems wit
h unbounded stochastic uncertainties. The control approach aims to shape probability density function of the stochastic states, while satisfying input and joint state chance constraints. Closed-loop stability is ensured by designing a stability constraint in terms of a stochastic control Lyapunov function, which explicitly characterizes stability in a probabilistic sense. The Fokker-Planck equation is used for describing the dynamic evolution of the states probability density functions. Complete characterization of probability density functions using the Fokker-Planck equation allows for shaping the states density functions as well as direct computation of joint state chance constraints. The closed-loop performance of the stochastic control approach is demonstrated using a continuous stirred-tank reactor.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
