Search results for "Bounded function"
showing 10 items of 508 documents
Computation of the Multivariate Oja Median
2003
The multivariate Oja median (Oja, 1983) is an affine equivariant multivariate location estimate with high efficiency. This estimate has a bounded influence function but zero breakdown. The computation of the estimate appears to be highly intensive. We consider different, exact and stochastic, algorithms for the calculation of the value of the estimate. In the stochastic algorithms, the gradient of the objective function, the rank function, is estimated by sampling observation. hyperplanes. The estimated rank function with its estimated accuracy then yields a confidence region for the true sample Oja median, and the confidence region shrinks to the sample median with the increasing number of…
Consensus for networks with unknown but bounded disturbances
2009
We consider stationary consensus protocols for networks of dynamic agents. The measure of the neighbors' states is affected by unknown but bounded disturbances. Here the main contribution is the formulation and solution of what we call the $\epsilon$-consensus problem, where the states are required to converge in a target set of radius $\epsilon$ asymptotically or in finite time. We introduce as a solution a dead-zone policy that we denote as the lazy rule.
Local and nonlocal weighted pLaplacian evolution equations with Neumann boundary conditions
2011
In this paper we study existence and uniqueness of solutions to the local diffusion equation with Neumann boundary conditions and a bounded nonhomogeneous diffusion coefficient g ≥ 0, {ut = div (g|∇u|p-2∇u) in ]0; T[×Ωg|∇u|p-2u·n = 0 on ]0; T[×∂Ω; for 1 ≤ p < ∞. We show that a nonlocal counterpart of this diffusion problem is ut(t; x)= ∫ω J(x-y)g(x+y/2)|u(t; y)-u(t; x)| p-2 (u(t; y)-u(t; x)) dy in ]0; T[× Ω,where the diffusion coefficient has been reinterpreted by means of the values of g at the point x+y/2 in the integral operator. The fact that g ≥ 0 is allowed to vanish in a set of positive measure involves subtle difficulties, specially in the case p = 1.
Sharp estimates for eigenfunctions of a Neumann problem
2009
In this paper we provide some bounds for the eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of R^n. To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.
On the existence of bounded solutions to a class of nonlinear initial value problems with delay
2017
We consider a class of nonlinear initial value problems with delay. Using an abstract fixed point theorem, we prove an existence result producing a unique bounded solution.
Convergence analysis of cubature Kalman filter
2014
This paper investigates the stability analysis of cubature Kalman filter (CKF) for nonlinear systems with linear measurement. The certain conditions to ensure that the estimation error of CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the MCKF is compared to the CKF by two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF while the MCKF is successfully able to estimate the sta…
Fiber Suspension Flows: Simulations and Existence Results
2016
Main result of this article is demonstrating the weak global in time well posedness result for the equations governing fiber suspension flows for sufficiently small initial data under mild assumptions about the nonlinear equation for fiber orientation dynamics and the constitutive law, thus extending the previous local in time results. The required estimate of growth of the H 2 norm is granted if the L ∞ norm of fiber orientation state variables remains bounded. This is the case for fiber orientation tensors.
Robust finite-time fuzzy H∞ control for uncertain time-delay systems with stochastic jumps
2014
Abstract This paper investigates the problem of robust finite-time H ∞ control for a class of uncertain discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi–Sugeno (T–S) model. Initially, the concepts of stochastic finite-time boundedness and stochastic finite-time H ∞ stabilization are presented. Then, by using stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastically finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level in a given finite-time interval. Furthermore, sufficient criteria on stochastic finite-time H ∞ stabilization using a fuzzy s…
Observer-based finite-time control for discrete fuzzy jump nonlinear systems with time delays
2013
This paper investigates the problem of observer-based finite-time H∞ control for a family of discrete jump nonlinear systems with time delays represented by Takagi-Sugeno (T-S) model. The main contribution of this paper is to design an observer-based finite-time H∞ controller such that the resulting closed-loop system is stochastic finite-time bounded and satisfies a prescribed H∞ disturbance attenuation level over the given finite-time interval. Sufficient criteria on stochastic finite-time H∞ stabilization via observer-based fuzzy state feedback are provided for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. A simulati…
Finite-time stabilization for discrete fuzzy jump nonlinear systems with time delays
2013
This paper is concerned with the problem of finite-time H∞ control for a class of discrete-time Markovian jump nonlinear systems with time delays represented by Takagi-Sugeno (T-S) model. First, by using fuzzy stochastic Lyapunov-Krasovskii functional approach, sufficient conditions are derived such that the resulting close-loop system is stochastic finite-time bounded and satisfies a prescribed H∞ disturbance attenuation level in a given finite-time interval. Second, sufficient criteria on stochastic finite-time H∞ stabilization via fuzzy state feedback are provided, and the fuzzy state feedback controller is designed by solving an optimization problem in terms of linear matrix inequalitie…