Approximate Solution for Some Continuous Optimal Control Problems Using Veita-Pell Polynomials
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1246Keywords:
Vieta-Pell polynomials, continuous optimal control problem, direct method, Lagrange multipliers, quadratic programming techniqueAbstract
In this paper, Veita-Pell polynomials (VPPs) are first presented with some interesting properties. These properties are utilized to construct a general explicit formula of their operational matrix of derivative. Then an appropriate direct technique is suggested for solving quadratic optimal control problems based on VPPs and the idea of state parameterization algorithm. The resulting performance index optimal value shows the proposed method is able to provide a good treatment with fast convergence. The effectiveness of the presented method is illustrated by solving three numerical examples. The obtained results show that as the number of basis functions VPPs increase the error in the solution by the present method will be decreased and it may exactly close with the analytical one. This is the main modification of the algorithm and this contribution in the using special basis functions in obtaining an approximate solution with minimum number of VPPs and satisfactory accuracy.
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