Results in Control and Optimization最新文献

This study focuses on optimization of pressure gradient on MHD peristaltic nanofluid flow by response surface methodology (RSM). The governing equations, including continuity, motion, nanoparticle, and concentration force are solved by disregarding inertial forces and employing the approximation of long-wavelength. The perturbation method is used to solve the resultant nonlinear coupled partial differential equation analytically. Mathematical and graphical outputs for concentration, temperature, and pressure rise, considering all physical parameters, are presented. Numerical computation is applied to assess expressions for friction forces and pressure rise. Magnetohydrodynamics has various applications in various microchannel designs for efficacious flow control in pumping fluids for both pulsating and non-pulsating continuous flow. Finally, Response Surface Methodology (RSM) is used for performing sensitivity analysis and its optimization. ANOVA tables are generated with the help of MINITAB-19 which is a statistical software. The sensitivity results are displayed in tabular and graphical form and concluded that M is more sensitive than other input parameters for $\Delta P$at the low level and the input parameter Nt is most sensitive among others at middle and high levels. Further, Temperature and pressure of the flow has different responses for various values of magnetic, thermophoresis and Brownian motion parameter.

This study introduces an innovative approach combining Taylor wavelet with quasilinearization, aiming to enhance the fractional-order tumor growth model. To explore the prediction of tumor growth, the fractional order Taylor wavelet (FOTW) technique is employed. Block pulse functions (BPFs) are used for constructing a fractional order operational matrix of integration. Next, the quasilinearization method is employed to transform the given equations into a linear algebraic system of equations. To show the performance of the FOTW based approach, the numerical results are obtained and discussed geometrically. The outcomes show that fractional models work more effectively, and can be further explored.

Pneumatic servo systems face challenges such as friction, compressibility, and nonlinear dynamics, necessitating advanced control techniques. Research suggests model-based, model-free, hybrid, and optimization-based methods have their strengths. Therefore, this study presents an optimal control strategy using Adaptive Domain Prescribed Performance Control (AD-PPC) cascaded with PID and optimized using the Evolutionary Mating Algorithm (EMA) for a pneumatic servo system (PSS). The goal is to achieve faster transient control and stable rod-piston positioning with minimal friction through the hysteresis phenomenon of the targeted proportional valve-controlled double-acting pneumatic cylinder (PPVDC) representing the PSS. The novel EMA optimizes the cascaded controller based on the tracking error as its objective function. Simulation studies verify the proposed AD-PPC-PID controller with the PPVDC model plant, iteratively optimized by the EMA. The analytical study compares this setup's control system and optimization model with the same control system model using alternative optimization methods. The testing employs step and multi-step signals for PPVDC's rod-piston position input. Results show that the EMA-tuned AD-PPC-PID outperforms AD-PPC-PID controller with other optimizers. For both input trajectory tests, EMA-tuned AD-PPC-PID shows faster response times, with average improvements of 30 % in settling times and 70 % in tracking performance metrics compared to other optimizers, making it robust for nonlinear system applications like PPVDC rod-piston positioning.

In this paper, we study an augmented Lagrangian-type algorithm called the Dislocation Hyperbolic Augmented Lagrangian Algorithm (DHALA), which solves an inequality nonconvex optimization problem. We show that the sequence generated by DHALA converges to a Karush–Kuhn–Tucker (KKT) point under the Mangasarian–Fromovitz constraint qualification. The contribution of our work is to consider a constraint qualification into this algorithm. Finally, we present some computational illustrations to demonstrate the performance our algorithm works.

The Malaria epidemic is a serious public health issue that is worrying to the affected people in the tropics and subtropical parts of the world. The alarming consequences of the disease have prompted the scientific communities to seek better ways to manage the disease. In Ghana, the accurate statistical estimate of the Malaria transmission parameters is paramount to the public Health to embark on a transmission reduction program but rarely exists. The study’s purpose is to undertake a comprehensive mathematical analysis of a newly designed compartmentalized vector-host Malaria model capturing the aquatic mosquito vector compartment and vaccinated human host for the goal of estimating the model’s parameters and the threshold $R_0$ computation and examining the associated bifurcation type that invokes at the Malaria-free state. The study thoroughly analyses the asymptomatic stability of the model to classify the respective behaviours at the equilibria. A sensitivity study of LHS-PRCC was undertaken to measure the variability in the threshold $R_0$. Further, the model was subjected to a comprehensive analysis to assess the impact of vaccines on the dynamics of the disease. The analysis showed that vaccines have a substantial impact in reducing the Malaria cases in Ghana. To have a more reliable and accurate estimation of the model parameters of Ghana and robust mitigating intervention protocols for public health officials, the Least square fitting approach is applied to data of Ghana for an extended period of 10 years, starting from 2010 to 2020, to estimate the model’s parameters. The Malaria model was further structured into an intervention model to provide tailored eradication strategies for curtailing the disease. To exemplify the cost-effective procedure for assessing the cost related to the identified interventions, the ACER and ICER were used to analyse the cost of each intervention per the benefit. The results from the analyses suggest that increasing accessibility and executing a control intervention of 8 as identified by the cost analysis by Public Health will assist in mitigating the disease with a comparatively minimal cost.

This paper presents a mathematical model aimed at elucidating the dynamics of fowl pox transmission within poultry populations. The model focuses on implementing control strategies to manage the spread of the disease, considering two primary modes of transmission: direct contact and transmission via mosquitoes. Our objective is to enhance understanding of disease propagation and to propose a control strategy aimed at minimizing the number of infected birds $I_b\left(t\right)$ and increasing the number of recovered birds $R_b\left(t\right)$ during the time interval $\left(t_0,t_f\right)$, while also minimizing the costs associated with implementing the control strategy. The proposed mathematical framework facilitates the integration of various control strategies to effectively manage fowl pox transmission dynamics. By employing Pontryagin’s maximum principle, efficient control measures are identified to mitigate the spread of the disease. Finally, numerical simulations are performed to verify the theoretical analysis using MATLAB.

This research focuses on the development, analysis, and simulation of fractional mathematical models to investigate the transmission dynamics of different phases of breast cancer. The suggested breast cancer model incorporates three often-used fractional operators in epidemiology: Caputo, Caputo–Fabrizio–Caputo, and Atangana–Baleanu–Caputo operators. In this study, the determination of the equilibrium point and its stability analysis is conducted using the Routh–Hurwitz criterion. Additionally, we examine the existence and uniqueness of solutions for the fractional system using Krasnoselskii’s and Banach fixed-point theory. Moreover, the global stability is discussed via the Ulam–Hyres criterion. Furthermore, the fractional models are being verified using reported occurrences of stage IV breast cancer among females in Saudi Arabia from 2004 to 2016. The real data is used to determine the values of the parameters that are fitted using the least squares error-minimizing methodology. Also, residuals and efficiency rates are computed for the integer as well as fractional-order models. Graphical representations are used to illustrate numerical results by examining different choices of fractional order parameters. Then, the dynamic characteristics of various stages of breast cancer are analyzed to demonstrate the impact of fractional order on breast cancer progression and how the rate of chemotherapy influences its behavior. We provide graphical results for a breast cancer model with effective parameters, resulting in fewer future incidences in the population of stages III and IV. Chemotherapy often raises the risk of cardiotoxicity, and our proposed model output reflects this. The goal of this study is to reduce the incidence of cardiotoxicity in chemotherapy patients while also increasing the pace of patient recovery. This research has the potential to significantly improve outcomes for patients and provide information on treatment strategies for breast cancer patients.

This study introduces a novel fractional-order spatio-temporal SEIR model for epidemic modeling, providing an advanced approach to understanding disease dynamics. Our model, categorizing the population into Susceptible (S), Exposed (E), Infected (I), and Recovered (R), incorporates fractional calculus to accurately reflect the complex, non-linear nature of infectious diseases. Key findings include the confirmation of the existence and uniqueness of the model’s solutions, ensuring reliability for epidemiological predictions. Through rigorous stability analysis at both disease-free and endemic equilibrium points, we identified critical parameters influencing epidemic outcomes. Numerical simulations reveal that the fractional order significantly impacts disease progression, offering valuable insights for intervention strategies.

In this paper, we analyze an automated manufacturing system modeled as a queueing system with multiple servers, differentiated vacation (DV) policy, customer impatience, and server failures. We consider the waiting servers policy, where the servers wait for a random duration before leaving for a vacation once the system gets empty. Upon their return, if no customers are waiting, the servers may leave for a second type-2 vacation of shorter duration. The system may experience breakdowns and require immediate repair. During the repair period, customers are served at a lower rate, and they become impatient during busy, vacation, and repair periods, abandoning the queue if their timer expires. Further, based on the queue length, arriving customers may either join the system or balk with some probability. We use the matrix analytic method to derive the steady-state probability of the system and several performance measures. Moreover, we illustrate the effect of different system parameters on various performance measures. Additionally, we develop a cost model and optimize the system capacity, number of servers, and service rates such that cost per unit time is minimized. Finally, we analyze the impact of system parameters on the cost through numerical examples.

The research presents a novel approach to inventory modelling, emphasizing stochastic demand and dynamic pricing strategies for a seasonal sales framework. The methodology divides the sales season into intervals, each associated with distinct pricing strategies influenced by stochastic factors. The study employ exponential smoothing for demand forecasting, optimizing inventory replenishment and dynamic pricing strategies through developed algorithms. Notably, the study determine the optimal smoothing parameter for demand forecasting, balancing responsiveness to recent demand patterns with long-term stability. Proposed research achieves a comprehensive framework empowering businesses to enhance competitiveness and profitability by addressing challenges of stochastic demand and dynamic pricing. Dynamic pricing strategies outperformed classical strategies, allowing businesses to respond promptly to demand fluctuations and optimize profit margins during sales seasons. Incorporating stochastic demand models enabled organizations to implement safety stock and buffer inventory levels effectively, mitigating risks associated with uncertain demand patterns. Real-time data analysis was crucial for adjusting price dynamics and making effective management decisions, leading to improved financial performance. The iterative nature of dynamic pricing strategies emphasized the importance of continuous refinement to adapt to evolving market dynamics. This approach enables data-driven decisions, adaptation to market fluctuations, and improved inventory management despite unpredictable demand. Ultimately, this study provides valuable insights and methodologies applicable across industries for efficient and profitable inventory management.