T. M. Agbaje^a,b, S. S. Motsa^a,* , S. Mondal^c,† , P. Sibanda^a

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-13, 2017, DOI:10.5098/hmt.9.36

Abstract In this work, we present a compliment of the spectral perturbation method (SPM) for solving nonlinear partial differential equations (PDEs) with applications in fluid flow problems. The (SPM) is a series expansion based approach that uses the Chebyshev spectral collocation method to solve the governing sequence of differential equation generated by the perturbation series approximation. Previously the SPM had the limitation of being used to solve problems with small parameters only. This current investigation seeks to improve the performance of the SPM by doing the series expansion about a large parameter. The new method namely the large parameter spectral perturbation… More >

Suthep Suantai^1,2, Zulqurnain Sabir^3,4, Muhammad Asif Zahoor Raja⁵, Watcharaporn Cholamjiak^6,*

CMC-Computers, Materials & Continua, Vol.75, No.1, pp. 2155-2170, 2023, DOI:10.32604/cmc.2023.034699

Abstract The purpose of this study is to present the numerical performances and interpretations of the SEIR nonlinear system based on the Zika virus spreading by using the stochastic neural networks based intelligent computing solver. The epidemic form of the nonlinear system represents the four dynamics of the patients, susceptible patients S(y), exposed patients hospitalized in hospital E(y), infected patients I(y), and recovered patients R(y), i.e., SEIR model. The computing numerical outcomes and performances of the system are examined by using the artificial neural networks (ANNs) and the scaled conjugate gradient (SCG) for the training of the networks, i.e., ANNs-SCG. The… More >

Aamir Shahzad¹, Ali Altalbe^2,*

Computer Systems Science and Engineering, Vol.46, No.1, pp. 853-871, 2023, DOI:10.32604/csse.2023.035575

Abstract The main idea behind the present research is to design a state-feedback controller for an underactuated nonlinear rotary inverted pendulum module by employing the linear quadratic regulator (LQR) technique using local approximation. The LQR is an excellent method for developing a controller for nonlinear systems. It provides optimal feedback to make the closed-loop system robust and stable, rejecting external disturbances. Model-based optimal controller for a nonlinear system such as a rotatory inverted pendulum has not been designed and implemented using Newton-Euler, Lagrange method, and local approximation. Therefore, implementing LQR to an underactuated nonlinear system was vital to design a stable… More >

Ahmed M. Elmogy^1,2,*, Wael M. Elawady²

Intelligent Automation & Soft Computing, Vol.36, No.1, pp. 385-400, 2023, DOI:10.32604/iasc.2023.032349

Abstract One of the great concerns when tackling nonlinear systems is how to design a robust controller that is able to deal with uncertainty. Many researchers have been working on developing such type of controllers. One of the most efficient techniques employed to develop such controllers is sliding mode control (SMC). However, the low order SMC suffers from chattering problem which harm the actuators of the control system and thus unsuitable to be used in many practical applications. In this paper, the drawbacks of low order traditional sliding mode control (FOTSMC) are resolved by presenting a novel adaptive radial basis function… More >

A. Jegatheesh^1,*, M. Germin Nisha², N. Kopperundevi³

Intelligent Automation & Soft Computing, Vol.36, No.1, pp. 745-760, 2023, DOI:10.32604/iasc.2023.028011

Abstract Interacting The highest storage capacity of a circular tank makes it popular in process industries. Because of the varying surface area of the cross-sections of the tank, this two-tank level system has nonlinear characteristics. Controlling the flow rate of liquid is one of the most difficult challenges in the production process. This proposed effort is critical in preventing time delays and errors by managing the fluid level. Several scholars have explored and explored ways to reduce the problem of nonlinearity, but their techniques have not yielded better results. Different types of controllers with various techniques are implemented by the proposed… More >

Aamir Shahzad^1,*, Shadi Munshi², Sufyan Azam², Muhammad Nasir Khan³

CMC-Computers, Materials & Continua, Vol.73, No.2, pp. 2897-2911, 2022, DOI:10.32604/cmc.2022.028441

Abstract The main objective of this research is to design a state-feedback controller for the rotary inverted pendulum module utilizing the linear quadratic regulator (LQR) technique. The controller maintains the pendulum in the inverted (upright) position and is robust enough to reject external disturbance to maintain its stability. The research work involves three major contributions: mathematical modeling, simulation, and real-time implementation. To design a controller, mathematical modeling has been done by employing the Newton-Euler, Lagrange method. The resulting model was nonlinear so linearization was required, which has been done around a working point. For the estimation of the controller parameters, MATLAB… More >

Muhammad Umar¹, Fazli Amin¹, Soheil Salahshour², Thongchai Botmart³, Wajaree Weera³, Prem Junswang^4,*, Zulqurnain Sabir¹

CMC-Computers, Materials & Continua, Vol.72, No.3, pp. 6185-6202, 2022, DOI:10.32604/cmc.2022.027970

Abstract The present study is related to design a stochastic framework for the numerical treatment of the Van der Pol heartbeat model (VP-HBM) using the feedforward artificial neural networks (ANNs) under the optimization of particle swarm optimization (PSO) hybridized with the active-set algorithm (ASA), i.e., ANNs-PSO-ASA. The global search PSO scheme and local refinement of ASA are used as an optimization procedure in this study. An error-based merit function is defined using the differential VP-HBM form as well as the initial conditions. The optimization of the merit function is accomplished using the hybrid computing performances of PSO-ASA. The designed performance of… More >

Ahmed M. Elmogy^1,2,*, Amany Sarhan², Wael M. Elawady²

CMC-Computers, Materials & Continua, Vol.72, No.3, pp. 5629-5641, 2022, DOI:10.32604/cmc.2022.025247

Abstract As most real world systems are significantly nonlinear in nature, developing robust controllers have attracted many researchers for decades. Robust controllers are the controllers that are able to cope with the inherent uncertainties of the nonlinear systems. Many control methods have been developed for this purpose. Sliding mode control (SMC) is one of the most commonly used methods in developing robust controllers. This paper presents a higher order SMC (HOSMC) approach to mitigate the chattering problem of the traditional SMC techniques. The developed approach combines a third order SMC with an adaptive PID (proportional, integral, derivative) sliding surface to overcome… More >

Abdul-Wahid A. Saif¹, Mohammad Ataur-Rahman¹, Sami Elferik¹, Muhammad F. Mysorewala¹, Mujahed Al-Dhaifallah^1,*, Fouad Yacef²

Intelligent Automation & Soft Computing, Vol.27, No.3, pp. 817-834, 2021, DOI:10.32604/iasc.2021.015932

Abstract In this paper, the formation control problem of a group of unmanned air vehicle (UAV) quadrotors is solved using the Takagi–Sugeno (T–S) multi-model approach to linearize the nonlinear model of UAVs. The nonlinear model sof the quadrotor is linearized first around a set of operating points using Taylor series to get a set of local models. Our approach’s novelty is in considering the difference between the nonlinear model and the linearized ones as disturbance. Then, these linear models are interpolated using the fuzzy T–S approach to approximate the entire nonlinear model. Comparison of the nonlinear and the T–S model shows… More >

Obadah Said Solaiman, Ishak Hashim^*

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1427-1444, 2021, DOI:10.32604/cmc.2020.012610

Abstract In this paper, we propose a fifth-order scheme for solving systems of nonlinear equations. The convergence analysis of the proposed technique is discussed. The proposed method is generalized and extended to be of any odd order of the form 2n − 1. The scheme is composed of three steps, of which the first two steps are based on the two-step Homeier’s method with cubic convergence, and the last is a Newton step with an appropriate approximation for the derivative. Every iteration of the presented method requires the evaluation of two functions, two Fréchet derivatives, and three matrix inversions. A comparison… More >