Results in Control and Optimization最新文献

This study aims to explore Ćirić-type generalized $F$-contractions, almost $F$-contractions, and the combination of these contractions in the framework of super metric spaces. These generalizations are significant because they hold where the usual metric conditions mayn’t be fulfilled. Using the iteration method, fixed point results have been obtained for these contractions, and through examples and applications to integral inclusions and contractions, we extend existing literature significantly. This extension offers new insights and demonstrates practical relevance.

This paper is a novel attempt to analyze different aspects of a two-strain epidemic model. The paper introduces a novel approach to analyzing a two-strain epidemic model, emphasizing the efficacy of combining non-pharmaceutical interventions and vaccination, particularly against new variants. Additionally, it presents a unique spatio-temporal model to assess spatial distribution of infections, offering fresh insights into how spatial factors influence disease transmission and control. The analysis involves stability analysis(local and global) and optimal control. Time-dependent social/non-pharmaceutical interventions coupled with vaccination of the susceptible class in the presence of both strains are analyzed using Pontryagin’s Maximum Principle. The numerical section shows the behavior of the infected class with and without control, the control intensity trend for the scenario when only non-pharmaceutical interventions (NPI) are practiced for the original strain, and when both NPI and vaccination are incorporated with the emergence of the new strain. The evaluation of the Incremental average ratio (IAR) and Incremental cost-effectiveness ratio (ICER) determines that NPI and vaccination as a combination is better and ideal in terms of costs incurred and effectiveness as a whole in averting infection in the presence of a new variant. Finally, we have also proposed a spatio-temporal pattern for the new strain model to analyze patterns using the finite element method by PDE Toolbox to show the effect of different initial conditions and geometry on the density of the infected population.

Restructuring the electricity market has led to the establishment of a competitive open market environment. The electricity market has introduced uncertainty and risk in the economic sector conventionally owned by the state. The power generated in the generating station is transferred to the distribution side in the power markets, which share a common transmission network. The power transfer will be in bulk amounts and needed to operate the electricity market securely and economically. The bulk amount of power transfer relies on accurately estimating Available Transfer Capability (ATC), representing the maximum allowable power flow through the existing transmission network while maintaining system reliability. The estimation of the ATC using a proposed hybrid method. The hybrid method comprises Repeated Power Flow (RPF) and Support Vector Regression (SVR) methods. The electricity market participants such as sellers and buyers submit bids to maximize their profit with the help of ATC values. The linear bid function is proposed to formulate participant strategies. Each participant will submit the availability of power requirement and willing price in the linear bid function. The Energy Valley Optimizer (EVO) algorithm is proposed to maximize the profit of each participant. The EVO algorithm efficiently explores a vast solution space, considering complex constraints and uncertainties inherent in the market dynamics to enhance economic gains. The proposed work is tested on the practical UPSEB (Uttar Pradesh State Electricity Board) 75-bus Indian utility system.

Load Frequency Control (LFC) and Voltage Control (VC) are critical aspects of hybrid generation systems. In this work, the performance comparison of three different control approaches for LFC and VC: Genetics Algorithm (GA)-tuned Proportional Integral Differentiator (PID), Particle Swarm Optimization (PSO)-PID, and a conventional PID controller is presented. Especially, the performance is assessed and analyzed for convergence speed and computational complexity for each approach. Mathematical framework for each approach is discussed, including the required equations for hybrid generation system. It is reported that the traditional PID controller exhibits fast convergence due to its direct adjustment of control parameters. Simulation results reveal that it requires manual tuning and has low computational complexity. In contrast, the GA-PID utilizes a GA optimization process which automatically tunes the PID gains. Although, it may require multiple generations to converge to the optimal solution, however, it offers better control performance. Moreso, it comes at the cost of higher computational complexity compared to the traditional PID controller. In contrast, the PSO-PID employs an algorithm for parameter optimization. It converges faster than the GA-PID but still requires more iterations than the traditional PID controller. Similar to the GA-PID, it has higher computational complexity due to fitness function evaluation and particle updates. The optimization results provide insights into the convergence speed and computational complexity trade-offs between the three control approaches. Practitioners in the field of hybrid energy systems can utilize the outcomes to make informed decisions based on their specific requirements and available computational resources.

A scam rumor is a false information that is spread in order to deceive individuals and organizations. These rumors frequently use people’s trust and emotions for illegal purposes to gain money or cause harm. This paper presents an optimal control strategy and a cost effectiveness analysis for a deterministic model designed to explain how false information, or ”Scam Rumor” spreads on social networking sites. This model accounts for the network’s informants’ actions. We evaluate the efficacy of tactics to stop the propagation of scam rumors via social media using optimal control theory. We also do numerical simulations to evaluate the benefits and drawbacks of applying the techniques we suggest, emphasizing their potential to improve the accuracy of online content.

This manuscript introduces a perturbation-free extremum-seeking control strategy specifically designed to enhance the operational performance of wind turbines under optimal conditions. The strategy employed utilizes a perturbation-free extremum-seeking approach to ensure the wind turbine farm operates at maximum power efficiency while also reducing power output fluctuations. By employing this control system, the wind turbine generators are maintained at their optimal power output level, effectively navigating through disturbances such as tower shadow, wind shear, and the erratic nature of wind speeds without introducing external perturbations.

The algorithm is adept at managing the blade pitch angles and the turbines’ rotational speed, ensuring a controlled and efficient operation. Furthermore, this paper outlines a perturbation-free method to optimize energy production and decrease fatigue loads, thereby extending the operational lifespan of a wind turbine. The superior operational efficiency of the wind turbine array generators achieved through this approach underscores its effectiveness.

The robustness and effectiveness of this perturbation-free control system are validated through comprehensive simulation tests on an array comprising four wind turbine generators. The outcomes of these simulations solidly back the extremum-seeking control system’s proficiency in reaching maximum power output without relying on perturbative methods, highlighting its innovative contribution to wind turbine efficiency optimization.

In this paper, an optimization problem (DP) is studied where the objective maps and the constraints are the difference of set-valued maps (abbreviated as SVMs). The higher-order $\sigma$-cone arcwise connectedness is described as an entirely new type of generalized higher-order arcwise connectedness for set-valued optimization problems. Under the higher-order contingent epiderivative and higher-order $\sigma$-cone arcwise connectedness suppositions, the higher-order sufficient Karush–Kuhn–Tucker (KKT) optimality requirements are demonstrated for the problem (DP). The higher-order Wolfe ($WD$) form of duality is investigated and the corresponding higher-order weak, strong, and converse theorems of duality are established between the primary (DP) and the corresponding dual problem by employing the higher-order $\sigma$-cone arcwise connectedness supposition. In order to demonstrate that higher-order $\sigma$-cone arcwise connectedness is more generalized than higher-order cone arcwise connectedness, an example is also constructed. As a special case, the results coincide with the existing ones available in the literature.

This paper introduces a fractional-order (FO) $SEIR$ epidemic model for respiratory diseases considering a non-human class $P\left(t\right)$ for pathogens to study the effects of fear and awareness programs on disease dynamics. Further, using the basic reproduction number ${ℛ}_0^{\alpha }$, the criteria for the extinction or persistence of the disease is established. Also, the conditions for Hopf bifurcation are derived, considering both FO ($\alpha$) and rate of pathogens $\eta$ as the bifurcation parameters. In addition, a detailed numerical simulation is performed to substantiate our theoretical results. The study of transmission dynamics of Tuberculosis (TB), a particular example of respiratory disease, is carried out in reference to the United States (US). Finally, we have estimated model parameters with the help of actual TB data from the US and then predicted the TB dynamics and disease control. It is pointed out that the fractional order can reduce the complexity of the model and better predict the dynamics of TB in the US than the integer order.

In this work, mathematical modeling of a nonlinear differential equation was studied to investigate the effect of vaccination on the spread of chickenpox. The proof of existence and uniqueness of the positive solution and invariant region showed that the model is epidemiologically sound. We established the disease-free and endemic equilibrium states and carried out a stability analysis of the disease-free and endemic equilibrium states of the model to gain insight into the dynamics of the model. The rate of vaccination and precaution for the spread of chickenpox was a factor that influenced the basic reproductive number, which was calculated using the next-generation matrix approach. Forecasts made via numerical simulation using the Laplace Adomian Decomposition method highlight the temporal impact of vaccination on curbing the chicken pox trend.

The problem of load frequency control (LFC) for power grids has received widespread attention in power industrial control. Ensuring the stability of the frequency is the primary concern that constrains the development of the electric power system. This paper presents a novel internal model control (IMC)- proportional-integral-derivative (PID) controller design method for LFC control systems, centered on pole-zero conversion. This method aims to simplify the system model's complexity and improve the system's performance. The IMC controller is approximated as a PID series compensator (high-order PID), with exact tuning formulas provided for various scenarios. These include single-area without or with reheat turbines, hydro turbines with transient droop compensators, wind turbines, and gas turbines. The tuning formulas are characterized by a single parameter, determined under robustness constraints and integrated time absolute error (ITAE). The proposed tuning method considers the generator rate constraint (GRC) and applies to multi-area single-source and multi-area multi-source power systems. The results of the simulation confirm that the controller tuning method presented in this paper has significant advantages over the existing design methods concerning robustness and anti-interference performance.