Fractional order maps are a hot research topic; many new mathematical models are suitable for developing new applications in different areas of science and engineering. In this paper, a new class of a 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The hyperchaotic map has no equilibrium and lines of equilibrium points, depending on the values of the system parameters. All of the chaotic attractors generated by the proposed fractional map are hidden. The system dynamics are analyzed via bifurcation diagrams, Lyapunov exponents, and phase portraits for different values of the fractional order. The results show that the fractional map has rich dynamical behavior, including hidden homogeneous multistability and offset boosting. The paper also illustrates a novel theorem, which assures that two hyperchaotic fractional discrete systems achieve synchronized dynamics using very simple linear control laws. Finally, the chaotic dynamics of the proposed system are stabilized at the origin via a suitable controller.

In this article, the position tracking control of the wheelchair upper-limb exoskeleton robotic system is investigated with the aim of rehabilitation of disabled people. Hence, the fuzzy nonsingular terminal sliding mode control method by using the state observer with a fixed-time convergence rate is designed in three main parts. In the first part, the fixed-time state observer is proposed for estimation of the states of the system. Secondly, the fixed-time convergence of position tracking error of the upper-limb exoskeleton robot system is examined by using the nonsingular terminal sliding mode control approach. In the third part, with the target of the improvement of the controller performance for removal of the chattering phenomenon which diminishes the controller performance, the fuzzy control method is used. Finally, the efficiency and proficiency of the proposed control method on the upper limb exoskeleton robotic system are demonstrated via the simulation results which are provided by MATLAB/Simulink software. In this part, simulation results are obtained based on different initial conditions in two examples using various desired values. Thus, it can be demonstrated that the proposed method applied to the upper-limb exoskeleton robot system is robust under various initial conditions and desired values.

In this paper, an adaptive neural network approach is developed based on the integral nonsingular terminal sliding mode control method, with the aim of fixed-time position tracking control of a wheelchair upper-limb exoskeleton robot system under external disturbance. The dynamical equation of the upper-limb exoskeleton robot system is obtained using a free and typical model of the robotic manipulator. Afterward, the position tracking error between the actual and desired values of the upper-limb exoskeleton robot system is defined. Then, the integral nonsingular terminal sliding surface based on tracking error is proposed for fixed-time convergence of the tracking error. Furthermore, the adaptive neural network procedure is proposed to compensate for the external disturbance which exists in the upper-limb exoskeleton robotic system. Finally, to demonstrate the effectiveness of the proposed method, simulation results using MATLAB/Simulink are provided.

In the past few years, the world has suffered from an untreated infectious epidemic disease (COVID-19), caused by the so-called coronavirus, which was regarded as one of the most dangerous and viral infections. From this point of view, the major objective of this intended paper is to propose a new mathematical model for the coronavirus pandemic (COVID-19) outbreak by operating the Caputo fractional-order derivative operator instead of the traditional operator. The behavior of the positive solution of COVID-19 with the initial condition will be investigated, and some new studies on the spread of infection from one individual to another will be discussed as well. This would surely deduce some important conclusions in preventing major outbreaks of such disease. The dynamics of the fractional-order COVID-19 mathematical model will be shown graphically using the fractional Euler Method. The results will be compared with some other concluded results obtained by exploring the conventional model and then shedding light on understanding its trends. The symmetrical aspects of the proposed dynamical model are analyzed, such as the disease-free equilibrium point and the endemic equilibrium point coupled with their stabilities. Through performing some numerical comparisons, it will be proved that the results generated from using the fractional-order model are significantly closer to some real data than those of the integer-order model. This would undoubtedly clarify the role of fractional calculus in facing epidemiological hazards.

The three-dimensional (3D) force sensor has become essential in industrial and medical applications. The existing conventional 3D force sensors quantify the three-direction force components at a point of interest or extended contact area. However, they are typically made of rigid, complex structures and expensive materials, making them hard to implement in different soft or fixable industrial and medical applications. In this work, a new flexible 3D force sensor based on polymer nanocomposite (PNC) sensing elements was proposed and tested for its sensitivity to forces in the 3D space. Multi-walled carbon nanotube/polyvinylidene fluoride (MWCNT/PVDF) sensing element films were fabricated using the spray coating technique. The MWCNTs play an essential role in strain sensitivity in the sensing elements. They have been utilized for internal strain measurements of the fixable 3D force sensor’s structure in response to 3D forces. The MWCNT/PVDF was selected for its high sensitivity and capability to measure high and low-frequency forces. Four sensing elements were distributed into a cross-beam structure configuration, the most typically used solid 3D force sensor. Then, the sensing elements were inserted between two silicone rubber layers to enhance the sensor’s flexibility. The developed sensor was tested under different static and dynamic loading scenarios and exhibited excellent sensitivity and ability to distinguish between tension and compression force directions. The proposed sensor can be implemented in vast applications, including soft robotics and prostheses’ internal forces of patients with limb amputations.

A hydraulic generator regulating system with electrical, mechanical, and hydraulic constitution is a complex nonlinear system, which is analyzed in this research. In the present study, the dynamical behavior of this system is investigated. Afterward, the input/output feedback linearization theory is exerted to derive the controllable model of the system. Then, the chaotic behavior of the system is controlled using a robust controller that uses a Chebyshev neural network as a disturbance observer in combination with a non-singular robust terminal sliding mode control method. Moreover, the convergence of the system response to the desired output in the presence of uncertainty and unexpected disturbances is demonstrated through the Lyapunov stability theorem. Finally, the effectiveness and appropriate performance of the proposed control scheme in terms of robustness against uncertainty and unexpected disturbances are demonstrated through numerical simulations.