Numerical solution of optimal control problem of the non-linear Volterra integral equations via generalized hat functions

Mirzaee, Farshid; Hadadiyan, Elham

doi:10.1093/imamci/dnw002

Cited by 2 publications

(3 citation statements)

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“…In Tables 4–6, a comparison is proposed between the approximate values of x ( t ), u ( t ) and normalℑ achieved by rationalized Haar wavelet collocation method (RHW) (Maleknejad and Ebrahimzadeh (2015)), generalized hat functions method (GHF) (Mirzaee and Hadadiyan (2017)) and our method, respectively. These reported results demonstrated confirm the high accuracy of the proposed scheme.…”

Section: Computational Resultsmentioning

confidence: 99%

“…Consider the following minimization of functional (Maleknejad and Ebrahimzadeh (2015))subject to the nonlinear Volterra integral equationThe analytical solution is given by x(t)=e−t2,u(t)=t, and ℑ=0. A comparison of the approximated values of normalℑ is made between the reported values obtained using Block-pulse series (BPS) (Shienyu (1990)), RHW (Maleknejad and Ebrahimzadeh (2015)), GHF (Mirzaee and Hadadiyan (2017)), and our method, in Table 7. Moreover, the absolute errors of state variable x ( t ) and control variable u ( t ) for k = 2, M = 7 are shown in Figure 5.…”

Section: Computational Resultsmentioning

confidence: 99%

“…Tang in (Tang (2015)) presented Chebyshev collocation method to solve OCPs by Volterra integral equations. F. Mirzaee and E. Hadadiyan (Mirzaee and Hadadiyan (2017)) solved this kind of problem using generalized hat functions. Also, the authors in (Maleknejad and Ebrahimzadeh (2014; 2015)) proposed Legendre wavelets method and rationalized Haar wavelets collocation method to solve the mentioned problems.…”

Section: Introductionmentioning

confidence: 99%

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Solution of optimal control problems governed by volterra integral and fractional integro-differential equations

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Ordokhani

Rabiei

et al. 2022

Journal of Vibration and Control

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In this manuscript, we investigate two categories of optimal control problems (OCPs), OPCs via fractional Volterra integro-differential equations and Volterra integral equations. Touchard wavelets as an appropriate class of bases are defined to develop a new hybrid scheme for the considered problems. To this approach, Riemann–Liouville fractional integral operator (RLFIO) of Touchard wavelets is achieved exactly using the Hypergeometric functions. Next, by approximating the fractional derivative of the state variables and control variables using the mentioned wavelet functions, applying RLFIO, collocation method, and Gauss–Legendre quadrature formula, the considered problems are inserted into systems of algebraic equations, which can be solved using “FindRoot” package in Mathematica software. Numerical results are presented that validate the theory and show the effectiveness of the established technique.

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