dynamical system

On the radial solutions of a p-Laplace equation with the Hardy potential

In this paper, we study the asymptotic behavior of radial solutions of the following quasi-linear equation with the Hardy potential $\Delta_p u+h(|x|)|u|^{p-2}u=0$, $x\in \mathbb{R}^{N}-\{0\}$, where $2<p<N$, $h$ is a radial function on $\mathbb{R}^{N}-\{0\}$ such that $h(|x|)=\gamma|x|^{-p}$, $\gamma>0$ and $\Delta_p u=\operatorname{div}\left(|\nabla u|^{p-2}\nabla u\right)$ is the $p$-Laplacian operator.  The study strongly depends on the sign of $\gamma-(\sigma/p^\ast)^p$ where $\sigma=(N-p)/(p-1)$ and $p^\ast=p/(p-1)$.

Application of a Fuzzy Particle Filter to Observe a Dynamical System States in Real Time

One of the key problems in the implementation of closed-loop control systems is to measure all states of a dynamic system, especially, when there are severe environmental conditions. Consequently, the use of certain types of sensors is impossible for technical or economic reasons. Also, in electromechanical systems, there are a lot of values that cannot be directly measured by physical sensors. Thus, mathematical algorithms named as observers and estimators are in use to calculate the states of the dynamic system utilizing math model and available set of sensors.

Influences of standard linear forms on characteristics of dynamic system with fuzzy modal controller

On the example of two-mass fuzzy control system the influence of characteristic polynomial’s roots on the characteristics of a dynamic system is investigated. The conclusions about the advisability of setting controller to the appropriate standard linear forms depending on the size of the error of system’s output coordinate.

Investigation of the defuzzification method influence on characteristics of the system with takagi-sugeno fuzzy controller

A dynamic system that consists of two subsystems is considered. The influence of defuzzification method on quality indicators of the system is investigated. A comparison of the main defuzzification methods is held

Research of dynamic system with unstable subsystem that has one root in the right half-plane

A two-mass system is investigated. It is considered as a set of dynamical subsystems. To switch between these subsystems, fuzzy controller is synthesised. The research is held for the case when one subsystem is unstable having one root in the right-hand side of the plane. The stability of the overall system, depending on the stability of the subsystems of which it is composed is examined. For this, a 3D hodograph is used. Quality indexes of the system with unstable subsystem are calculated. The case when the system operates under external perturbations is consider.