Nonlinear model predictive control based on Nelder Mead optimization method

Chagra, Wassila; Degachi, Hajer; Ksouri, Mekki

doi:10.1007/s11071-017-3544-8

Cited by 13 publications

(7 citation statements)

References 29 publications

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“…For the particular case of the Gompertz model, three optimization algorithms were tested, notable for performing the search for parameters in the shortest possible time starting from initial conditions. The Nelder–Mead simplex algorithm was designed to solve nonlinear optimization problems without restrictions and does not require derivative computation of the function under test [ 27 ]. Nonlinear regression algorithm is a type of regression to determine parameters of a model that requires fitting real data [ 28 ].…”

Section: Methodsmentioning

confidence: 99%

Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México

2021

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The present work is focused on modeling and predicting the cumulative number of deaths from COVID-19 in México by comparing an artificial neural network (ANN) with a Gompertz model applying multiple optimization algorithms for the estimation of coefficients and parameters, respectively. For the modeling process, the data published by the daily technical report COVID-19 in Mexico from March 19th to September 30th were used. The data published in the month of October were included to carry out the prediction. The results show a satisfactory comparison between the real data and those obtained by both models with a R 2 > 0.999. The Levenberg–Marquardt and BFGS quasi-Newton optimization algorithm were favorable for fitting the coefficients during learning in the ANN model due to their fast and precision, respectively. On the other hand, the Nelder–Mead simplex algorithm fitted the parameters of the Gompertz model faster by minimizing the sum of squares. Therefore, the ANN model better fits the real data using ten coefficients. However, the Gompertz model using three parameters converges in less computational time. In the prediction, the inverse ANN model was solved by a genetic algorithm obtaining the best precision with a maximum error of 2.22% per day, as opposed to the 5.48% of the Gompertz model with respect to the real data reported from November 1st to 15th. Finally, according to the coefficients and parameters obtained from both models with recent data, a total of 109,724 cumulative deaths for the inverse ANN model and 100,482 cumulative deaths for the Gompertz model were predicted for the end of 2020.

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Section: Methodsmentioning

confidence: 99%

Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México

2021

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“…In [36], the neural network is used to determine the solution of the minimization problem. In [37], the Nelder Mead algorithm was applied which leads to global solution by using far initialization. The simulations gave optimal results with least computation time for SISO and MIMO models.…”

Section: Model Predictive Control Design For Wiener Modelmentioning

confidence: 99%

Nonlinear Model Predictive Control for pH Neutralization Process based on SOMA Algorithm

Degachi¹,

Chagra²,

Ksouri³

2018

ijacsa

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Abstract-In this work, the pH neutralization process is described by a neural network Wiener (NNW) model. A nonlinear Model Predictive Control (NMPC) is established for the considered process. The main difficulty that can be encountered in NMPC is solving the optimization problem at each sampling time to determine an optimal solution in finite time. The aim of this paper is the use of global optimization method to solve the NMPC minimization problem. Therefore, we propose in this work, to use the Self Organizing Migrating Algorithm (SOMA) to solve the presented optimization problem. This algorithm proves its efficiency to determine the optimal control sequence with a lower computation time. Then the NMPC is compared to adaptive PID controller, where we propose to use the SOMA algorithm to formulate the PID in order to determine the optimal parameters of the PID. The performances of the two controllers based on the SOMA algorithm are tested on the pH neutralization process.

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“…Thus approaches that combine the advantages of global and local search algorithms are of interest [3]. The Nelder Mead Simplex method is a derivative free local optimization technique used to minimize or maximize an objective function in an unconstrained multidimensional space [28]. In the case of a bi-variable function, the simplex forms a triangle and the technique performs a pattern search which computes function values at every vertex.…”

Section: A Improving Accuracy With Local Searchmentioning

confidence: 99%

“…The triangle size is then progressively decreased and the coordinates of the least points are determined. The NM-Simplex method is computationally efficient and robust [28,29]. In this paper Nelder-Mead Simplex method is used to refine the solution found by the PSO for the ANN training problem.…”

Section: A Improving Accuracy With Local Searchmentioning

confidence: 99%

A New Quantum Tunneling Particle Swarm Optimization Algorithm for Training Feedforward Neural Networks

Amali¹,

Dinakaran²

2018

IJISA

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In this paper a new Quantum Tunneling Particle Swarm Optimization (QTPSO) algorithm is proposed and applied to the training of feedforward Artificial Neural Networks (ANNs). In the classical Particle Swarm Optimization (PSO) algorithm the value of the cost function at the location of the personal best solution found by each particle cannot increase. This can significantly reduce the explorative ability of the entire swarm. In this paper a new PSO algorithm in which the personal best solution of each particle is allowed to tunnel through hills in the cost function analogous to the Tunneling effect in Quantum Physics is proposed. In quantum tunneling a particle which has insufficient energy to cross a potential barrier can still cross the barrier with a small probability that exponentially decreases with the barrier length. The introduction of the quantum tunneling effect allows particles in the PSO algorithm to escape from local minima thereby increasing the explorative ability of the PSO algorithm and preventing premature convergence to local minima. The proposed algorithm significantly outperforms three stateof-the-art PSO variants on a majority of benchmark neural network training problems.

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Nonlinear model predictive control based on Nelder Mead optimization method

Cited by 13 publications

References 29 publications

Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México

Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México

Nonlinear Model Predictive Control for pH Neutralization Process based on SOMA Algorithm

A New Quantum Tunneling Particle Swarm Optimization Algorithm for Training Feedforward Neural Networks

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