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The world is currently facing a pandemic called COVID-19 which has drastically changed our human lifestyle, affecting it badly. The lifestyle and the thought processes of every individual have changed with the current situation. This situation was unpredictable, and it contains a lot of uncertainties. In this paper, the authors have attempted to predict and analyze the disease along with its related issues to determine the maximum number of infected people, the speed of spread, and most importantly, its evaluation using a model-based parameter estimation method. In this research the Susceptible-Infectious-Recovered model with different conditions has been used for the analysis of COVID-19. The effects of lockdown, the light switch method, and parameter variations like contact ratio and reproduction number are also analyzed. The authors have attempted to study and predict the lockdown effect, particularly in India in terms of infected and recovered numbers, which show substantial improvement. A disease-free endemic stability analysis using Lyapunov and LaSalle's method is presented, and novel methods such as the convalescent plasma method and the Who Acquires Infection From Whom method are also discussed, as they are considered to be useful in flattening the curve of COVID-19.

The diabetes mellitus model (DMM) is explored in this study. Many health issues are caused by this disease. For this reason, the integer order DMM is converted into the time delayed fractional order model by fitting the fractional order Caputo differential operator and delay factor in the model. It is proved that the generalized model has the advantage of a unique solution for every time t. Moreover, every solution of the system is positive and bounded. Two equilibrium states of the fractional model are worked out i.e. disease free equilibrium state and the endemic equilibrium state. The risk factor indicator, R 0 is computed for the system. The stability analysis is carried out for the underlying system at both the equilibrium states. The key role of R 0 is investigated for the disease dynamics and stability of the system. The hybridized finite difference numerical method is formulated for obtaining the numerical solutions of the delayed fractional DMM. The physical features of the numerical method are examined. Simulated graphs are presented to assess the biological behavior of the numerical method. Lastly, the outcomes of the study are furnished in the conclusion section.

This study aims at investigating the dynamics of sexually transmitted infectious disease (STID), which is serious health concern. In so doing, the integer order STID model is progressed in to the time-delayed non-integer order STID model by introducing the Caputo fractional derivatives in place of integer order derivatives and including the delay factors in the susceptible and infectious compartments. Moreover, unique existence of the solution for the underlying model is ensured by establishing some benchmark results. Likewise, the positivity and boundedness of the solutions for the projected model is explored. The basic reproduction number is is found out for the model. The time-delayed non-integer order STID model holds two steady states, namely, the STID free and endemic steady state. The model stability is carried out at the steady states. The non-standard finite difference (NSFD) technique is hybridized with the Grunwald Letnikov (GL) approximation for finding the numerical solutions of the time-delayed non-integer order STID model. The boundedness and non-negativity of the numerical scheme is confirmed. The simulated graphs are presented with the help of an appropriate test example. These graphs show that the proposed numerical algorithm provides the positive bounded solutions. The article is ended with productive outcomes of the study.

During the actual transportation process, overhead cranes are always affected by the double-pendulum effect, resulting in excessive swinging angles that affect the control performance of the anti-swing system. Moreover, the viscous resistance, air resistance, and swing angle suppression force encountered during transportation have uncertainties and cannot be accurately fed back to the controller’s input, resulting in poor swing angle suppression capability. In order to suppress the undesired swinging of the hook and load, this paper proposes an adaptive coupling anti-swing control strategy with enhanced swing angle suppression under initial input constraints. Specifically, more system parameters are included in the design of the coupling signal, and a sine term is introduced to adjust the oscillation of the hook and load swing angle. At the same time, a hyperbolic tangent term is introduced to suppress the driving force of the overhead crane to prevent excessive driving force from affecting the control performance. Furthermore, for the problem of uncertain parameters, an adaptive law is used to estimate the uncertain parameters online, ultimately designing an adaptive coupling anti-swing controller with enhanced swing angle suppression under initial input constraints. The asymptotic stability of the equilibrium point of the closed-loop system is proven using the Lyapunov method and LaSalle’s invariance principle. Through extensive experimental simulations, the proposed control strategy demonstrates good control performance.

In this paper, a non-stationary enhanced swing angle suppression control strategy is proposed to address the issue of excessive swinging angles during the transportation process of a three-dimensional overhead crane. Firstly, in response to the substantial non-stationary initial swing angle resulting from the abrupt increase in driving force during the startup of the overhead crane, we have devised a time-varying damping resistance model. This model is specifically designed to curtail the rapid force surge, subsequently diminishing the swing angle of the payload. Secondly, during the transport phase of the overhead crane, we have established an augmented coupling signal between the displacement tracking error and the payload swing angle tracking error. Drawing upon the principles of energy dissipation, we have devised a nonlinear sway controller. Next, the closed-loop stability of the control system is validated through the use of Lyapunov’s method and the LaSalle invariance principle. Finally, the proposed control strategy’s effectiveness has been substantiated through simulation analysis and physical experiments. This approach not only proves capable of effectively suppressing excessive payload swing angles during the transportation process of the overhead crane but also facilitates the rapid and precise positioning of the payload. This significantly enhances the efficiency of the overhead crane’s transport operations.

This paper presents a unified treatment of the optimal control of under-actuated two-link manipulators. Firstly, a nonlinear invertible transfer is introduced to simplify design of controller, then several optimal control laws are established by maximum principle. Controller for swing-up area is based on performance index, while controller for attractive area is based on LQR (linear quadric regulator). It is proved that optimal control is not singular, invariant sets are obtained by theoretical analysis. The strategy for Acrobat is to use optimal control law to pump manipulators into linearizable area, then switch control law to LQR, which drives system to up-straight position. Local and global stability were analyzed in detail under control strategy using LaSalle's invariance principle and WCLF (non-smooth control Lyapunov function). Simulation and comparison with previous results show that the proposed approach here is valid and of advantages.

The term, Festschrift, is defined as a volume of learned articles or essays by colleagues and admirers, serving as a tribute to a scholar. The recognition of LaSalle D. Leffall, Jr., M.D., F.A.C.S. adds credence to the merits of such a tribute.

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle’s Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance.

Mathematical model is needed to study the epidemiology of tuberculosis. Here we have proposed a model that is more realistic. We are exhibiting a theoretical framework for getting the control and eradication methodologies to minimize the number of infectious tuberculosis cases in the community. For this purpose, the model population has been compartmentalized and the consequential model equations have been solved analytically. Numerical Simulation has been given to validate the results obtained by the theoretical approach. The effect of latent periods on the epidemics of tuberculosis with respect to population density has been studied. The equilibrium points of the model are calculated and their stability is established by using the 'Basic Reproduction number'. It is observed that when basic reproduction number is less or equal to unity, the disease-free equilibrium point (DEF) is globally asymptotically stable, while when it is greater to unity, the endemic equilibrium point (EE) is globally asymptotically stable i.e., illness will persist in the population and epidemic will turn out to be endemic. Also, it is obtained that compactness of people decides the infection rate of tuberculosis i.e. the risk of instability of disease free equilibrium increases as the population density increases.

Motivated by a phenomenon of phase transition in a model of alignment of self-propelled particles, we obtain a kinetic mean-field equation which is nothing more than the Smoluchowski equation on the sphere with dipolar potential. In this self-contained article, using only basic tools, we analyze the dynamics of this equation in any dimension. We first prove global well-posedness of this equation, starting with an initial condition in any Sobolev space. We then compute all possible steady states. There is a threshold for the noise parameter: over this threshold, the only equilibrium is the uniform distribution, and under this threshold, the other equilibria are the Fisher-von Mises distributions with arbitrary direction and a concentration parameter determined by the intensity of the noise. For any initial condition, we give a rigorous proof of convergence of the solution to a steady state as time goes to infinity. In particular, when the noise is under the threshold and with nonzero initial mean velocity, the solution converges exponentially fast to a unique Fisher-von Mises distribution. We also found a new conservation relation, which can be viewed as a convex quadratic entropy when the noise is above the threshold. This provides a uniform exponential rate of convergence to the uniform distribution. At the threshold, we show algebraic decay to the uniform distribution.