Predefined-Time Control of Full-Scale 4D Model of Permanent-Magnet Synchronous Motor with Deterministic Disturbances and Stochastic Noises

This paper presents a predefined-time convergent robust control algorithm that allows the control designer to set the convergence time in advance, independently of initial conditions, deterministic disturbances, and stochastic noises. The control law is consequently designed and verified by simulations for a full-scale 4-degrees-of-freedom (4D) permanent-magnet synchronous motor (PMSM) system in cases of a disturbance-free system with completely measurable states, a disturbance-free system with incompletely measurable states, a system with incompletely measurable states in the presence of deterministic disturbances, and a system with incompletely measurable states in the presence of both deterministic disturbances and stochastic noises. Numerical simulations are provided for the full-scale 4D PMSM system in order to validate the obtained theoretical results in each of the considered cases. To the best of our knowledge, this is the first attempt to design a predefined-time convergent control law for multi-dimensional systems with incompletely measurable states in the presence of both deterministic disturbances and stochastic noises.

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if $\xi <1$ ξ < 1 ; whereas the epidemic cannot go out of control if $\xi >1$ ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

Numerical Simulation of Free Convection in a Three-Dimensional Enclosure Full of Nanofluid with the Existence a Magnetic Field

Blood glucose automatic regulation achievement depends on the robustness of the used control algorithm. However, some constraints were encountered due to the human glucose-insulin regulatory system’s complexity. It is proposed to tackle such a goal through the development of a robust synergetic control algorithm. An adaptive approach is integrated into this synergetic control scheme to handle disturbances and parameters variations. Multiple meal disturbances often occur daily as well as some other stochastic noises making efficient glucose regulation a tough challenge addressed in this paper via a new synergetic scheme. Simulation results show a robust function during multiple meal disturbances with good noise rejection.

Asymptotic properties of a population model with Allee effects in random environments

In this research, we probe the influences of two common types of stochastic noises in the environment, namely, white noise and telephone noise, and put forward a stochastic differential equation population model with Allee effects. We analyze some asymptotic behaviors of the model, including extermination, persistence and invariant measure. Some vital functions of white noise and telephone noise on these asymptotic behaviors of the model are discovered and numerically expounded.