A Survey of Probabilistic Methods for Dynamical Systems with Uncertain Parameters.

1986 ◽  
Author(s):  
J. L. Bogdanoff ◽  
F. Kozin
Keyword(s):  
Dynamical Systems ◽  
Probabilistic Methods ◽  
Uncertain Parameters

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

Robust Design of Structures with Uncertain Parameters and Frequency Constraints Using Non-Probabilistic Methods

2014 ◽  
Vol 936 ◽  
pp. 1479-1484
Author(s):  
Ji Yun Chen ◽  
Yan Luo ◽  
Dong Huan Liu
Keyword(s):  
Robust Design ◽  
Measurement Errors ◽  
Design Method ◽  
Probabilistic Methods ◽  
Structural Performance ◽  
Stochastic Methods ◽  
Uncertain Parameters ◽  
Vibration Frequencies ◽  
Design Variables ◽  
Robust Design Method

The structural physical properties are often uncertain due to manufacture errors, measurement errors and other factors. Consequently, the vibration frequencies and corresponding eigenvectors are also uncertain. Robust design selects suitable design variables so that structural performance is insensitive to the various causes of variation without eliminating possible variations of variables. In practice robust design methods can be classified into probabilistic methods and non-probabilistic methods respectively. A new non-probabilistic robust design method based on the set theoretical convex method is presented in the present paper. The method not only inherits the advantages of existing non-stochastic methods, but also conquers the disadvantages of these methods.

External synchronization of two dynamical systems with uncertain parameters

2010 ◽  
Vol 53 (3) ◽  
pp. 731-740 ◽  
Author(s):  
QingKai Han ◽  
XiaoYu Sun ◽  
XiaoGuang Yang ◽  
BangChun Wen
Keyword(s):  
Dynamical Systems ◽  
Uncertain Parameters

scholarly journals Designing the Adaptive Tracking Controller for Uncertain Fully Actuated Dynamical Systems with Additive Disturbances Based on Sliding Mode

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Chi Nguyen Van
Keyword(s):  
Dynamical Systems ◽  
Tracking Control ◽  
Control Method ◽  
Sliding Mode ◽  
Control Law ◽  
Uncertain Parameters ◽  
Transient Time ◽  
Vertical Movements ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

This paper addresses the problem of adaptive tracking control for uncertain fully actuated dynamical systems with additive disturbance (FDSA) based on the sliding mode. We use the adaptive mechanism to adjust the uncertain parameters in sliding mode control law which can be switched to two modes depending on the sliding surface. By choosing appropriately the parameters in control law, the desired transient time can be obtained without effects of uncertain parameters and additive disturbances. The chattering phenomenon can be minimized by a chosen constant. This control method is applied to the angles tracking control of the twin rotor multi-input multi-output system (TRMS) which have nonlinear characteristics, the input torque disturbances and the coupling between the horizontal and vertical movements. The simulation and experimental results are presented that validate the proposed solution.

Finitary Probabilistic Methods in Econophysics

2009 ◽  
Author(s):  
Ubaldo Garibaldi ◽  
Enrico Scalas
Keyword(s):  
Probabilistic Methods
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