On comparison between iterative methods for solving nonlinear optimal control problems

Jafari, Hossein; Ghasempour, Saber; Băleanu, Dumitru

doi:10.1177/1077546315590039

Cited by 14 publications

(7 citation statements)

References 21 publications

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“…wherẽk(t) = (̃1 ,k (t), … ,̃2 n,k (t)), the parameters D and P i,j have been defined in Equation (9), and nonhomogeneous term Z j,k in the kth step is determined by using the information of previous steps as in Equation (18). In addition, linear first-order ODEs at each step of the recursive process are completely decoupled for every j( j = 1, 2, … , 2n) so that they can be solved in parallel.…”

Section: Design Of Optimal Controllermentioning

confidence: 99%

“…Recently, some semianalytical techniques have been introduced such as homotopy perturbation method, Adomian decomposition method, and modified variational iteration method. Jafari et al have compared these methods for a class of nonlinear OCPs. They proved that these methods are equivalent, which means they use the same iterative formula to obtain the approximate/analytical solution.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Jajarmi

Băleanu

2018

Optim Control Appl Methods

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Summary This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two‐point boundary value problems is solved iteratively instead of solving the coupled nonlinear two‐point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower‐order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.

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Section: Design Of Optimal Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Jajarmi

Băleanu

2018

Optim Control Appl Methods

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“…The HPM can be applied to integro-differential equation (Elbeleze et al, 2016), linear and nonlinear NewellWhitehead-Segel equations (Nourazar et al, 2017), nonlinear optimal control problems (Jafari et al, 2016), integral equations (Elzaki and Alamri, 2016;Hasan and Matin, 2017), nonlinear wave-like equations with variable coefficients (Gupta et al, 2013), boundary value problems (Opanuga et al, 2017), the quadratic Riccati differential equation (Aminikhah and Hemmatnezhad, 2010), Boussinesq-like equations (Fernández, 2014) and others (Sakar et al, 2016;Soori et al, 2015;Qureshi et al, 2017;Zhang et al, 2014;Najafi and Edalatpanah, 2014;Roy et al, 2015;Abou-Zeid, 2016).…”

Section: Introductionmentioning

confidence: 99%

Improvement of the homotopy perturbation method to nonlinear problems

Alzaidi¹,

Alderremy²

2018

Int. J. Phys. Sci.

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This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations.

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“…1 Therefore, finding the optimal solution for these systems is interesting to many researchers. [2][3][4][5][6][7][8][9][10] Although the optimal control problem for linear systems without delays was solved in the 1960s, 11 the optimal control problem for linear systems with delays is still open, depending on the delay type, specific system equation, criterion, etc. 12 Kharatishvili extended the Pontryagin maximum principle to time-delay systems and obtained conditions for optimality.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets

Mohammadzadeh

Lakestani

2017

Optim Control Appl Methods

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SummaryThis paper proposes a new numerical approach for finding the solution of linear time-delay control systems with a quadratic performance index using new hybrid functions. This method is based on a hybrid of block-pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side. The excellent properties of the hybrid functions together with the operational matrices of integration, product, and delay are presented. Using these matrices, the solution of the optimal control of delay systems is reduced to the solution of algebraic equations. Because of the sparsity nature of these matrices, this method is computationally very attractive and reduces CPU time and computer memory. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The effectiveness of the method and the accuracy of the solution are shown in comparison with some other methods by illustrative examples.

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On comparison between iterative methods for solving nonlinear optimal control problems

Cited by 14 publications

References 21 publications

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Improvement of the homotopy perturbation method to nonlinear problems

Optimal control of linear time‐delay systems by a hybrid of block‐pulse functions and biorthogonal cubic Hermite spline multiwavelets

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