Hybrid functions approach for nonlinear constrained optimal control problems

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An approximate method for solving fractional optimal control problems by hybrid functions (2018, methodology): “The Riemann–Liouville fractional integral operator for the hybrid of block-pulse and Bernoulli polynomials is utilized to reduce the solution of the FOCP’s to a nonlinear programming one (Elnegar and Kazemi, 1998; Mashayekhi et al., 2012).”
Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis (2020, methodology): “…100 0 u21ðtÞ þ u22ðtÞ þ u23ðtÞ dt The approximate results for functional J of the present technique together with using quasilinearization and Chebyshev polynomials (Jaddu, 2002), themethod based on hybrid of block-pulse, and Bernoulli polynomials (Mashayekhi et al., 2012) are reported in Table 7.”
Numerical solution of the fractional Bagley‐Torvik equation by using hybrid functions approximation (2016, methodology): “Function approximation If f 2 L2Œ0, 1 and the best approximation of f by using the hybrid of block-pulse functions and Bernoulli polynomials is PN Mf , then [33] f ' P Mf D M X”
A numerical solution for fractional optimal control problems via Bernoulli polynomials (2016, methodology): “For approximating an arbitrary time function the advantages of Bernoulli polynomials over Legendre polynomials are given by Mashayekhi et al. (2012).”