Results in Control and Optimization最新文献

This study provides a comprehensive exploration of the qualitative analysis of a hybrid system of pantograph equations with fractional order and a p-Laplacian operator. The existence of the solution of the system is explicitly established within the context of Riemann–Liouville’s fractional order operator, employing the Arzelà–Ascoli theorem for validation. The establishment of uniqueness criteria is accomplished by the utilization of the Banach contractive technique. In addition, the examination of solution stability is conducted using the Hyers–Ulam (HU) stability technique. In order to enhance the credibility of our main conclusions, we have included a representative and illustrative example in the concluding section of the study. This work serve to offer a thorough and applicable comprehension of the mathematical framework that has been proposed.

Switched-mode DC–DC converters are required to maintain constant output under uncertainties and variations in input voltage and load. The controller’s robustness is crucial in such systems, and hence various controllers have been proposed in the past few decades for DC–DC converter control. Fractional order PID controllers have attracted the attention of researchers due to their robustness and flexibility in control of power converters. Such controllers use fractional orders of integration and differentiation. Complex order controllers are the generalized form of the fractional order PID controllers and have complex orders of integration and differentiation. These controllers are very robust in the control of nonlinear systems with time-varying parameters. But complex order controllers have been very sparingly used in power electronic control. This paper proposes a complex order PI controller with a complex order integrator for controlling DC–DC buck and boost converters. The complex PID controller has four parameters to be tuned. The complex order PI controller is designed by optimization using the metaheuristic Cohort Intelligence algorithm. The results are compared with that of a fractional-order PID controller. It was observed that the complex PI controller gave a better response than the FOPID controller and was more robust to parameter variations.

This paper discusses an optimal managerial approach regarding stock control in a manufacturing-inventory scenario. The selling price and inventory level in showrooms may impact customers’ demand. The fall in selling price creates additional demand, while shown inventory also positively enhances demand. In this paper, demand is influenced by the selling price during the productive phase and the displayed stock in idle time. The significance of selling price and stock on profit goal may not be inherited from that of the demand function. The production rate varies negatively against the inventory on hand. Instead of taking cost minimization or the profit maximization objective, this paper executes an optimization approach on the profit-cost ratio function, sharpening the manufacturer’s goal. The numerical solution and sensitivity analysis on optimal outcomes succeed the analytical solution in Mathematica software. Numerical results indicate that the profit-cost ratio rises with selling price, suppressing the negative impact of the selling price on demand. Also, the profit-cost ratio shows a concave curve for the production cycle, ensuring a global maximum for the objective function.

Background:

Efficient control of liquid levels in interconnected tank systems is a fundamental challenge in various industries, including chemical processes, wastewater treatment, and manufacturing. The traditional approach to achieving precise control has relied on Proportional–Integral–Derivative (PID) controllers, whose performance largely depends on tuned parameters. However, tuning PID controllers for complex and nonlinear systems like coupled tanks remains a challenging task. In recent years, nature-inspired optimization algorithms have gained prominence in control system design. The tree seed optimization (TSO), inspired by the dispersion of tree seeds in search of optimal growth conditions, has shown promise in solving complex optimization problems. This study seeks to explore the application of TSO in tuning PID controllers for coupled tank systems.

Methodology:

This research employs the TSO to optimize PID controller parameters for enhanced liquid-level control in coupled tank systems. The optimization process involves integrating performance metrics and closed-loop gain constraints to achieve optimal control of coupled tank systems. The imposed constraints aim to ensure robustness and system stability in the face of uncertainties and disturbances. Besides, $\mu$ analysis quantifies the robustness of the system by assessing its ability to tolerate uncertainties.

Findings:

Simulation studies conducted in this research verify the efficacy of the proposed TSO-based approach for tuning PID controllers in coupled tank systems. Compared with various methods, the TSO consistently yields better control performance, reduces settling time, and minimizes overshoot. The robustness of the optimized controllers is also evaluated, showing the ability to handle varying operating conditions effectively.

The present study explores the cost analysis for machine repair problem of queueing system using two-threshold control policies with discouragement and differentiated vacation. The way repairmen offer service has been established by two-threshold control policies based on queue size, with randomly distributed vacations of type $A_1$ (full vacation) and type $A_2$ (working vacation). Prior to the queue length being less than the lower threshold, both repairmen are on $A_1$ type vacations. One repairman remains on $A_1$ type vacation while the second repairman takes $A_2$ type vacation if the queue length is in the intermediate range of the two thresholds. If the queue length is at or exceeds the upper threshold, both repairmen serve the queue to the best of their abilities. Meanwhile, during $A_1$ and $A_2$ types of vacations, failing machines exhibit impatience, which is a common occurrence in getting the service. It is supposed that vacation and repair time are exponentially distributed. The recursive method is utilized to calculate steady-state system probabilities. Furthermore, several metrics have been defined to measure the effectiveness of the system. A cost model is developed using system performance data for cost analysis. The Fibonacci search algorithm (FSA) and an artificial bee colony (ABC) are used to find the optimal value for the choice of variables with the lowest expected cost. A real-world instance demonstrating the implementation of the proposed model in practice will be shown at the end.

The selection of Ph.D (Doctor of Philosophy) supervisor is always a vital and interesting problem in academia and especially for students who want to carry out Ph.D. Nowadays, selecting a supervisor for Ph.D in a scientific manner becomes a challenge for any student because of the variety of options available to the scholar. In this context, the present study aims to formulate a model for Ph.D. supervisor selection from the offered alternatives in an academic institute. A hybrid multi-criteria decision making (MCDM) framework has been applied to select the suitable supervisor of the student’s preferred criteria under interval-valued intuitionistic fuzzy (IVIF) scenario. The IVIF Analytic Hierarchy Process (AHP) has been employed to prioritize the criteria, whereas IVIF Technique for order preference by similarity to ideal solution (TOPSIS) technique is engaged to rank the available supervisors based on criteria weight. A set of eight criteria and five alternatives have been considered for modeling the problem. Moreover, the potential criteria are weighted and ranked by the multiple decision makers in the present study. To examine the consistency and robustness of the proposed integrated approach, sensitivity analysis and comparative analysis have been carried out. From all the analyses, it can be conferred that the suggested approach is quite useful to apply in different decision-making scenarios.

Of late, the exponential rise in the global population is driving higher energy demand. However, the rapid depletion of conventional fossil fuels and growing environmental concerns have prompted the evolution of alternative energy sources. To this end, Microgrid (MG) with Renewable Energy Sources (RES) has emerged as popular means of small-scale localized power grid. However, planning of MG operation poses challenges due to the inherent variability and stochasticity in RES power output and energy demand. On account of this, the present study introduces a Stochastic Energy Management Strategy (SEMS) for a grid-connected MG incorporating Micro-Turbine, Fuel-Cell, RES, Battery Energy Storage, and electrical and heat energy demand. The stochasticity of RES is forecasted through a hybrid prediction model (sARIMA-GRU) and the uncertain demand is estimated via 'Monte Carlo Simulation.' The proposed problem is formulated as a dynamic non-linear stochastic optimization problem. It seeks to minimize the expected value of MG operational cost satisfying the practical constraints. Addressing this, a newly developed ‘Artificial Electric Field Algorithm (AEFA)' is utilized. Several case studies are performed to assess MG operation under varied operating conditions. Moreover, the present study analyses the impact of uncertainty on energy contribution from DER, grid dependency, and MG operation cost. Comparative analysis reveals that sARIMA-GRU outperforms other contemporary prediction models. It is noteworthy that the superior prediction accuracy of sARIMA-GRU leads to lower MG operation costs. Moreover, statistical analysis and convergence confirm the proficiency of applied AEFA over state-of-the-art Grey Wolf Optimization and Firefly Algorithm in solving the proposed problem.

This study develops a mathematical link between pharmacokinetics and fractional calculus, emphasizing on metformin’s complex metabolic activities in diverse body areas. Our study proposes and evaluates a metformin kinetics model that incorporates homogenous dimensionality in the Caputo sense. To explore the uniqueness and existence of solutions, we adopt the Banach and Schauder fixed point theorems. The study includes equilibrium points, asymptotic stability in respect to certain parameters, and Lyapunov stable solutions. In addition, we investigate Ulam-type stability for the generalized model. The research finishes with a thorough theoretical analysis based on the generalized Adam–Bashforth–Moulton (A-B-M) technique, laying the groundwork for future empirical validation.

This paper focuses on the multi-objective Travelling Salesman Problem for which the aim is to find the set of efficient solutions. To obtain this Pareto set's solutions, a novel metaheuristic named DM4-PMO is proposed. The DM4-PMO is based on the first enhancement of the new Dhouib-Matrix-4 (DM4) method and composed of two steps. First, a weighted sum function with a multi variation of weights is used to find the first non-dominated pareto frontier solutions. Second, a lexicographical resolution is applied in some non-dominated solutions found in the first Pareto frontier to generate the final Pareto frontier solutions. The performance of the proposed approach is demonstrated by the experiment on two-objective problems that are taken from TSP-LIB and DIMACS datasets. The test results show that the proposed DM4-PMO is robust, fast, and simply structured, and obtain a Pareto non-dominated set solutions in short computational times using very few user-defined parameters.

A new method for approximate solution of ill-posed inverse problems of reconstructing images of objects with angular resolution exceeding the Rayleigh criterion is proposed and justified, i.e. with super resolution. Angular super-resolution allows you to obtain images of objects with increased clarity and distinguish previously invisible details of images of complex objects. In addition, on this basis, the probability of correct solutions to problems of object recognition and identification increases. Mathematically, the problem is reduced to solving the linear Fredholm integral equation of the first kind of convolution type. Solutions are sought with additional conditions in the form of restrictions on the location and size of the desired radiation source, which makes it possible to regularize the problem. The method is a development of one of the parameterization methods the algebraic method. The solution is sought in the form of a representation of the desired function in the area where the source is located in the form of a series expansion over the input sequence of orthogonal functions with unknown coefficients. Thus, the inverse problem is parameterized and reduced to searching for expansion coefficients. The presented method is based on the use of a priori information about the localization area of the radiation source, or on an estimate of the location and size of this area obtained by scanning the viewing sector with a goniometer system. Using zero values of the function describing the source outside this region, for systems based on antenna arrays it is possible to find tens and even hundreds of expansion coefficients of the desired function in a Fourier series. The solution is constructed in the form of an iterative process with a consistent increase in the number of functions used in the expansion until the solution remains stable. The adequacy and stability of the solutions was verified during numerical experiments using a mathematical model. The results of numerical studies show that the presented methods of digital processing of received signals make it possible to achieve an effective angular resolution 3–10 times higher than the Rayleigh criterion. The proposed method makes it possible to miniaturize the antenna system without degrading its characteristics. Compared to known ones, it is relatively simple, which allows it to be used by systems in real time.