An International Journal of Optimization and Control: Theories & Applications (IJOCTA)

Adaptive MIMO fuzzy PID controller based on peak observer

Kemal Uçak — 2023-07-09

In this paper, a novel peak observer based adaptive multi-input multi-output (MIMO) fuzzy proportional-integral-derivative (PID) controller has been introduced for MIMO time delay systems. The adaptation mechanism proposed by Qiao and Mizumoto [1] for single-input single-output (SISO) systems has been enhanced for MIMO system adaptive control. The tracking, stabilization and disturbance rejection performances of the proposed adaptation mechanism have been evaluated for MIMO systems by comparing with non-adaptive fuzzy PID and classical PID controllers. The obtained results indicate that the introduced adjustment mechanism for MIMO fuzzy PID controller can be successfully deployed for MIMO time delay systems.

Optimal C-type filter design for wireless power transfer system by using support vector machines

Haris Calgan — 2023-07-09

The rapid increase in the number of Electrical Vehicles (EVs) will bring difficulties in the management of charging process and pose serious grid problems at low voltage levels. Particularly, with employment of wireless power transfer (WPT) system in a charging station, harmonic interference will increase. The main reason of that poor power quality lies on high frequency square wave output of transmitter side of WPT. In this study, a support vector machine (SVM) is proposed to design an optimal C-type passive filter in order to mitigate voltage and current total harmonic distortions (THD) of WPT system. Hereby, SVM-based model is constructed which consists of THD indices and power factor (PF) as outputs whereas filter parameters are inputs. The main aim of optimization process is minimization of distortions and correction of PF while searching the filter parameters. Particle swarm optimization (PSO) algorithm is employed to find the optimal filter parameters. To show the efficiency of proposed method, simulation studies are carried out on Matlab^®/Simulink^TM environment. It is observed that voltage total harmonic distortion (THD_v) and current total harmonic distortion (THD_i) are calculated as 1.03%, 2.23%, respectively, and the power factor is improved to 0.995% when the designed C-type filter is utilized.

On the regional boundary observability of semilinear time-fractional systems with Caputo derivative

Khalid Zguaid — 2023-07-09

This paper considers the regional boundary observability problem for semilinear time-fractional systems. The main objective is to reconstruct the initial state on a subregion of the boundary of the evolution domain of the considered fractional system using the output equation. We proceed by providing a link between the regional boundary observability of the considered semilinear system on the desired boundary subregion, and the regional observability of its linear part, in a well chosen subregion of the evolution domain. By adding some assumptions on the nonlinear term appearing in the considered system, we give the main theorem that allows us to reconstruct the initial state in the well-chosen subregion using the Hilbert uniqueness method (HUM). From it, we recover the initial state on the boundary subregion. Finally, we provide a numerical example that backs up the theoretical results presented in this paper with a satisfying reconstruction error.

Single-drone energy efficient coverage path planning with multiple charging stations for surveillance

Atalay Celik — 2023-07-13

Drones have started to be used for surveillance within the cities, visually scanning the predefined zones, quickly detecting abnormal states such as fires, accidents, and pollution, or assessing the disaster zones. Coverage Path Planning (CPP) is a problem that aims to determine the most suitable path or motion plan for a vehicle to cover the entire desired area in the task. So, this paper proposes a novel two-dimensional coverage path planning (CPP) mathematical model with the fact that a single drone may need to be recharged within its route based on its energy consumption, and the obstacles must be avoided while constructing the route. Our study aims to create realistic routes for drones by considering multiple charging stations and obstacles for surveillance. We tested the model for a grid example based on the scenarios obtained by changing the layout, the number of obstacles and recharging stations, and area size using the Python Gurobi Optimization library. As a contribution, we analyzed the impact of the number of existing obstacles and recharging stations, the size and layout of the area to be covered on total energy consumption, and the total solution time of CPP in our study for the first time in the literature, through a detailed Scenario Analysis. Results show that the map size and the number of covered cells affect the total energy consumption, but different layouts with shuffled cells are not effective. The area size to be covered affects the total computation time, significantly. As the number of obstacles and recharging stations increases, the computation time decreases up to a certain limit, then stabilizes.

Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators

İlknur Koca — 2023-07-19

A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.

A study on the approximate controllability results of fractional stochastic integro-differential inclusion systems via sectorial operators

Kaliraj Kalimuthu — 2023-07-19

The study deals with the findings of the outcome of the approximate controllability results of inclusion type fractional stochastic system in Banach space with the order of the fractional system varrho in (1,2). At first, we implement Bohnenblust-Karlin's fixed point technique to deduce the required conditions on which the fractional system with inital conditions is approximately controllable, and there by, we postulate the sufficient conditions for extending the obtained results to the system with nonlocal conditions.

Fractional fuzzy PI controller using particle swarm optimization to improve power factor by boost converter

Metin Demirtas — 2023-07-27

The power circuit of AC voltage controller capable of operating at a leading, lagging, and unity power factor is studied by a lot of researchers in the literature. Circuits working with high switching frequency are known as power factor correctors (PFCs). The single-phase boost converter has become the most popular topology for power factor correction (PFC) in general purpose power supplies. Power factor correction circuit provides conventional benefits to electric power systems. The benefits are the reduction of power factor penalty and utility bill and power loss. Therefore, a boost converter power factor correction scheme is presented in this paper. A PI, fuzzy logic PI and fractional order PI (FOPI) controllers are used to fix an active shaping of input current of the circuit and to improve the power factor. The controller parameters (coefficients) are optimized using the Particle Swarm Optimization (PSO) algorithm. Average current mode control (ACMC) method is used in the circuit. The converter circuit consists of a single-phase bridge rectifier, boost converter, transformer and load. A mathematical model of the plant is required to design the PI controller. A model for power factor correction circuit is formed in MATLAB/Simulink toolbox and a filter is designed to reduce THD value. The proposed model is simulated using a combination of PI, fuzzy logic and FOPI controllers. The control scheme is applied to 600 Watt PFC boost converter to get 400 Volt DC output voltage and 0.99 power factor. The input voltage is 230 V_RMS with 50 Hz. The combination of FOPI and PI controller has the best solution to control the power factor according to PI and fuzzy controllers.

Prediction of anemia with a particle swarm optimization-based approach

Arshed A. Ahmad — 2023-07-28

Healthcare enables the maintenance of health through some physical and mental care for the prevention, diagnosis and treatment of disease. Diagnosis of anemia, one of the most common health problems of the age, is also very ambitious. Whereas, pathological individuals could be predicted through various biomedical variables using some appropriate methods. In order to estimate these individuals just by taking into account biological data, particle swarm optimization (PSO) and support vector machine (SVM) clustering techniques have been merged (PSO-SVM). In this respect, the dataset provided has been divided into five clusters based on anemia types consisting of 539 subjects in total, and the anemia values of each subject have been recorded according to corresponding biomedical variables taken as independent parameters. The findings of the PSO-SVM method have been compared to the results of the SVM algorithm. The hybrid PSO-SVM method has proven to be quite effective, particularly in terms of the high predictability of clustered disease types. it is possible to lead the successful creation of appropriate treatment programs for diagnosed patients without overlooking or wasting time during treatment.

Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

Mohamed Houas — 2023-07-29

In this paper, we discussed the existence, uniqueness and Ulam-type stability of solutions for sequential coupled hybrid fractional differential equations with two derivatives. The uniqueness of solutions is established by means of Banach's contraction mapping principle, while the existence of solutions is derived from Leray-Schauder's alternative fixed point theorem. Further, the Ulam-type stability of the addressed problem is studied. Finally, an example is provided to check the validity of our obtained results.

Regional enlarged controllability of a fractional derivative of an output linear system

Rachid Larhrissi — 2023-07-29

This new research aims to extend the topic of the enlarged controllability of a fractional output linear system. Thus, we characterize the optimal control by two methods, ensuring that the Riemann-Liouville fractional derivative of the final state of the considered system lies between two given functions on a subregion of the evolution domain. Firstly, we transform the considered problem into the saddle point using the Lagrangian multiplier approach. Then, in the second one, we provide the technique of the subdifferential, which allows us to present the cost-explicit formula of the minimum energy control. Moreover, we construct an algorithm of Uzawa type to illustrate the theoretical results obtained through numerical simulations.

The effect of fractional order mathematical modelling for examination of academic achievement in schools with stochastic behaviors

Pelin Yaprakdal Uzun — 2023-07-29

Academic achievement is very important, as it enables students to be well-equipped for professional and social life and shapes their future. In the case of a possible academic failure, students generally face many cognitive, social, psychological, and behavioral problems. This problem experienced by the students has been addressed with the mathematical model in this study. This mathematical model will be handled with the help of the fractional operator, and the existence, uniqueness, and positivity of the solutions to the model equation system will be examined. In addition, local and global stability analyses of the equilibrium points of the model are planned. Numerical simulations are performed with different values of fractional orders and densities of randomness. This study is very important in terms of its original and multidisciplinary approach to a subject in the field of social sciences.

Some stability results on non-linear singular differential systems with random impulsive moments

Arumugam Vinodkumar — 2023-07-29

This paper studies the exponential stability for random impulsive non-linear singular differential systems. We established some new sufficient conditions for the proposed singular differential system by using the Lyapunov function method with random impulsive time points. Further, to validate the theoretical results' effectiveness, we finally gave two numerical examples that study with graphical illustration and an additional example involving matrices with complex entries, proving the results to be true in that case as well.

The solvability of the optimal control problem for a nonlinear Schrödinger equation

Nigar Yildirim Aksoy — 2023-07-29

In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.