Results in Control and Optimization最新文献

This study presents an innovative approach by integrating adaptive sliding mode control strategies with fractional order modeling to address the challenge of reducing Aedes aegypti mosquito populations, the primary vector of Dengue - a widespread and debilitating disease. By employing the Atangana-Baleanu-Caputo fractional operator to model the dynamics of the mosquito population, we achieve a more precise representation of complex and non-linear behaviors. The motivation behind adopting the Adaptive Sliding Mode Control (ASMC) approach lies in the critical need to efficiently control Aedes aegypti mosquito populations, a key step in combating the prevalence of dengue. The ASMC method dynamically adjusts control parameters based on evolving conditions, enhancing its adaptability to the changing dynamics of mosquito populations.The Lyapunov stability theorem ensures the reliability of tracking convergence and control structure. Additionally, we implement the Toufik Atangana method to solve both state and adjoint fractional differential equations using the ABC derivative operator. This incorporation adds a novel dimension to the study, providing a comprehensive framework for addressing the intricate dynamics inherent in the Aedes aegypti mosquito population. To assess the effectiveness of the proposed strategy, a numerical performance index is introduced at the end of the abstract. This index justifies the controller’s efficacy by comparing it to other conventional controllers. The inclusion of this quantitative measure reinforces the significance of the proposed strategy in the context of dengue prevention and control efforts.

Employing an improved Leslie-Gower model, the Allee impact on the predator population and the fear influence on the prey population, a mathematical model of the interaction involving two populations, prey and predator, has been explored in the current work. The influence of the memory effect on the evolving behaviour of the model is integrated using a well-known fractional operator known as the Caputo fractional derivative of order (0, 1]. We were inspired to do this study because further research is desired to fully comprehend the dynamics of the Allee impact, fear, and Caputo fractional order. The innovative aspect of the current work is the consideration of the Caputo fractional derivative, which enhances the consistency domain of the system. To support the model's biological resilience and accuracy, the existence, uniqueness, positivity, and boundedness of the solution are provided. On the origin, axial, and interior, four distinct types of equilibrium points are distinguished along with the prerequisites for their existence. We additionally stated about the Hopf bifurcation of our proposed model at the interior equilibrium point in terms of fractional order and the fear influence as the bifurcation factors. To illustrate how various biological characteristics affect the dynamics of the solutions, numerical simulations are offered.

This present paper considers the dynamics of two criminal gangs in a criminally active population. In our deterministic approach, we present the gang rivalry model to measure the impact of rivalry intensities at low and moderately high initiation rates. The qualitative and quantitative properties of the models are investigated using appropriate techniques that have proven to be effective. Based on the numerical simulation study, the initiation rates are observed to play a key role in the rise and fall of rivalry intensities in the criminally active period, which is characterized by a low level of law enforcement. Furthermore, this study reveals that by reducing the initiation rate between susceptible individuals and criminal gang groups, the rivalry intensities will be impacted for the overall public safety.

This paper meticulously examines, with a keen focus, the intricate correlation between global unmanned aerial vehicle (UAV) regulations and the dynamic evolution of autonomy levels. Through a comprehensive investigation of the foundational components of UAVs, encompassing motors, propellers, flight control systems, and communication protocols, the study unveal the complex interactions that shape regulatory frameworks on a global scale. Expanding on this thorough exploration, the paper delves deeply into the critical role played by cutting-edge vision and mapping technologies, such as cameras and LiDAR sensors, in the ongoing endeavour to push the boundaries of autonomy. Furthermore, it explores subtle nuances in regulatory approaches across diverse regions, shedding light on the various factors influencing the development and implementation of UAV regulations. The paper also highlights the collaborative efforts within the industry and academia to address emerging challenges, fostering a deeper understanding of the synergies required for sustained advancements. Additionally, it delves into the implications of evolving regulatory landscapes on the broader drone ecosystem, including potential impacts on innovation, safety, and societal acceptance. Moreover, the paper critically assesses the current state of international cooperation in establishing standardized guidelines for UAV operations, providing insights into the potential harmonization of regulations to facilitate seamless global integration. By weaving together these multifaceted aspects, the paper not only offers valuable perspectives on the dynamic progression of UAV regulations but also significantly contributes to our nuanced understanding of the continuous advancements in autonomous control technology for these aerial platforms.

Models involving four species with prey refuge and type I responses have been studied with recommendations on their extension to include either type II or type III responses. However, models with Holling type II responses are de-stabilizing according to most studies. In this paper, therefore, a multi-species ecological system that includes a prey refuge and a Holling type III functional response is analyzed, to study the effect of reserved zones in enhancing the dynamical stability of the proposed system. The Routh-Hurwitz (RH) criterion and the eigenvalue technique are used to study the local stabilities. On the other hand, global stabilities have been studied using the Lyapunov technique. Numerical simulations have been carried out using the Matlab ode45 solver software to verify the analytical results. The findings show that refuge plays a significant part in improving the dynamic stability of the system.

Investigation of a mathematical model of malaria is considered in this manuscript. The concerned problem is investigated via Caputo–Fabrizio fractal fractional derivative. We derive the necessary conditions for the existence and uniqueness of solution for the proposed model of malaria. A powerful numerical procedure called Adams–Bashforth method is utilized for the simulations of our results. The considered technique is an excellent mathematical tool which is more efficient than the Euler and RK4 method. To discuss the dynamics of considered model, we provided the graphical presentations of our results by using various fractals and fractional orders values.

Process of finding the “best estimate” from noisy signals amounts to “filtering out” the noise. Many methods exist to filter the unwanted noise. A tried and tested method is to use a Kalman Filter which not only cleans up the signals but can also be used to provide signal estimates, for use in reduced order feedback control. Typically, Kalman filter gains are computed using the Linear Quadratic Regulator theory. Reduced order feedback control has been applied in aircraft control problems. One such application area is in synthetic load alleviation, structural loads that arise due to gusts and or control surface deflections. Aircraft structural load alleviation necessitates the use of robust feedback control. The controllers are required to provide load alleviation in cases where the feedback signals are contaminated with noise or missing due to sensor failures. In this paper a method of computing the Kalman gains for the purposes of reduced order feedback is presented, which completely specifies the error dynamics of the estimator in terms of its eigenvalues and associated eigenvectors. The state estimator synthesized using the proposed approach has excellent noise rejection properties and shown to be robust and can be successfully used in reduced order state feedback control, specifically in Aircraft Structural Load Alleviation control schemes. The proposed scheme demonstrates reduction in structural loads.

In this study, a novel method known as the Haar wavelet collocation method (HWCM) is used to analyze the mathematical model of Chlamydia transmission in the United States. We use dependent variables with various parameters, such as birth rate, mortality rate, and recovery rate, etc., to explore the nature of the Chlamydia disease in susceptible unvaccinated individuals, susceptible vaccinated individuals, infected, treated, and recovered individuals. The ordinary differential equations (ODEs) in this model are coupled nonlinear. In this method, the Chlamydia model is converted into a system of non-linear algebraic equations using properties of the operational matrix of Haar wavelets. Later, the Newton–Raphson approach is used to extract the unknown coefficients. Mathematica software has been used for all calculations. Tables and graphs contain tabulated results of calculations. As a result, it can be seen that the current approach is more precise than those used in the literature. Also, we discuss the effect of different parameters on susceptible unvaccinated individuals, susceptible vaccinated individuals, infected, treated, and recovered individuals through graphs.

In this paper, a compartmental model for the transmission of the co-infection of cholera and malaria was developed and analyzed. The reproduction numbers for each sub-model and the full model were calculated. In order to study the impact of each disease on the other, a sensitivity analysis was carried out and its results show that malaria infection is linked to an increased risk of cholera, whereas cholera infection is not associated with an increased risk of malaria. A set of seven variables’ controlling strategies, ranging from vector control to water sanitation and treatment, were added to the model; and their effect have been studied using the optimal control technique. Numerical simulations show the impact of these controlling strategies on the reduction of the new infections in humans and vectors as well as the reduction of the Cholera vibrio concentration in the environment. In order to find the most cost-effective controlling strategy, and all the three major cost-effectiveness analysis techniques were implemented to our model after we categorized all the controlling strategies into three scenarios, namely Cholera controlling strategy, Malaria controlling strategy, and Cholera–Malaria controlling strategy. The numerical results show that the most cost-effective controlling strategy in reducing the number of new infection is the vector control strategy.

In this paper, we have proposed and analysed a mathematical model to study the effects of impulsive input of contaminants in soil on the dynamics of interacting species system consisting of contaminants, soil-nutrients, plant biomass and herbivore population in order to investigate the criteria for the survival or extinction of plant biomass and herbivore population. The uptake function for herbivore population considered in the model of the paper shows saturation effect and this type of uptake function behave linearly with respect to plant biomass for low density. Also, the saturation for large plant biomass is a reflection of the limited herbivore capability or perseverance when the plant biomass is abundant. Therefore, the uptake function considered in this paper is more natural to lotka volterra and holling type functional responses. We have shown that the plant–herbivore extinction periodic solution exists and also the plant–herbivore extinction periodic solution is locally and globally stable if the impulsive depletion rate of nutrients due to contaminants is more than some critical value. Further, it is concluded that if the impulsive input period for contaminants is increased and impulsive depletion rate of nutrients due to contaminants is decreased then both the plant and herbivore population will survive otherwise they will tend to extinction.