Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model

Sabir, Zulqurnain; Ali, Mohamed R.; Raja, Muhammad Asif Zahoor; Shoaib, Mohammed; Núñez, Rafaél Artidoro Sandoval; Sadat, R.

doi:10.1007/s00366-021-01427-2

Cited by 30 publications

(4 citation statements)

References 54 publications

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“…the ANN-GAAS solver is accomplished to perform the highly nonlinear singular systems [ 46 , 47 ], biological differential models [ 48 , 49 ], nonlinear dynamics of the models [ [50] , [51] , [52] ], fractional differential model [ 53 , 54 ], cylindrical nonlinear Schrödinger equation [ 55 ], and pseudoplastic nanofluid flow [ 56 ].…”

Section: Future Research Directionmentioning

confidence: 99%

Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model

Sabir,

Baleanu,

E Alhazmi

et al. 2023

Heliyon

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Section: Future Research Directionmentioning

confidence: 99%

Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model

Sabir,

Baleanu,

E Alhazmi

et al. 2023

Heliyon

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“…However, the main limitation of numerical solutions is that stability and robustness conditions cannot be ensured in a deterministic way. Other numerical algorithms that can be useful for solving complex nonlinear MPC problems are presented in [31][32][33][34] which have been used to solve complex nonlinear differential equations and partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

An MPC-LQR-LPV Controller with Quadratic Stability Conditions for a Nonlinear Half-Car Active Suspension System with Electro-Hydraulic Actuators

et al. 2022

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The active suspension system of a vehicle manipulated using electro-hydraulic actuators is a challenging nonlinear control problem. In this research work, a novel Linear Parameter Varying (LPV) State-Space (SS) model with a fictional input is proposed to represent a nonlinear half-car active suspension system. Four different scheduling parameters are used to embed the nonlinearities of both the suspension and the electro hydraulic actuators to represent its nonlinear behavior. A recursive least squares (RLS) algorithm is used to predict the future behavior of the scheduling parameters along the prediction horizon. A Model Predictive Control-Linear Quadratic Regulator (MPC-LQR) is implemented as the control strategy and, to ensure stability, Quadratic Stability conditions are imposed as Linear Matrix Inequalities (LMI) constraints. Furthermore, the inclusion of attraction sets to overcome the conservative performance imposed by the Quadratic Stability conditions is included, as well as a terminal set were the switching between the MPC and the LQR controller is made. Simulations results for the half-car active suspension model over a typical road disturbance are tested to show the effectiveness of the proposed MPC-LQR-LPV controller with quadratic stability conditions in terms of comfort and road-holding.

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“…Shoaib et al [ 4 ] used neural networks to explore the generation of entropy under the influence of MHD and thermal radiation. Sabir et al [ 5 ] used a computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to describe the fourth-order nonlinear system of the Emden–Fowler model. Uddin et al [ 6 ] showed how to integrate magnetic and radiation impacts to comprehend the research of a Maxwell Nano-liquid thin film stream over a stretchable and spinning disk using LM-NN-based computational intelligence.…”

Section: Introductionmentioning

confidence: 99%

Neuro-Computing for Hall Current and MHD Effects on the Flow of Micro-Polar Nano-Fluid Between Two Parallel Rotating Plates

et al. 2022

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The present works focus on the effects of electric and magnetic fields on the flow of micro-polar nano-fluid between two parallel plates with rotation under the impact of Hall current (EMMN-PPRH) has considered by using Artificial Neural Networks with the scheme of Levenberg–Marquardt backpropagation (ANN-SLMB). The nonlinear PDEs are transformed into nonlinear ODEs by employing similarity variables. By varying different parameters such as coupling parameter, electric parameter, rotation parameter, viscosity parameter, Prandtl number and the Brownian motion parameter, a dataset for recommended ANN-SLMB is produced for numerous scenarios through utilizing homotopy analysis method (HAM). The ANN-SLMB training, testing and validation technique have been used to analyze the approximate solution of individual cases, and the recommended model has matched for confirmation. After that, regression analysis, MSE, and histogram investigations were utilized to validate the proposed ANN-SLMB. The recommended technique is distinguished nearest of the suggested and reference findings, with an accuracy level ranging from 10 −09 to 10 −11 .

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Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model

Cited by 30 publications

References 54 publications

Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model

Heuristic computing with active set method for the nonlinear Rabinovich–Fabrikant model

An MPC-LQR-LPV Controller with Quadratic Stability Conditions for a Nonlinear Half-Car Active Suspension System with Electro-Hydraulic Actuators

Neuro-Computing for Hall Current and MHD Effects on the Flow of Micro-Polar Nano-Fluid Between Two Parallel Rotating Plates

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