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This paper determines the state trajectory of a dynamic system over a period to optimize a given performance index. A one-step second derivative hybrid method based on the combination of Lucas and first Boubaker polynomials as basis functions is formulated for the solution of optimal control problems via the forward-backward sweep method. The technique is used to generate a set of hybrid schemes at selected grid and off-grid points with implementation in block form. The stability and convergence of the new method is discussed and the accuracy of the method is tested on some numerical examples. The results obtained correspond to a large extent with the results obtained by the exact solution. Bi-bases function, Block method, First Boubaker polynomials, Lucas polynomial, Optimal control problem
Olamiposi et al. (Wed,) studied this question.