Derivative-orthogonal wavelets for discretizing constrained optimal control problems

E. Ashpazzadeh, B. Han, M. Lakestani and M. Razzaghi

International Journal of Systems Science, 2020, vol. 51, issue 5, 786-810

Abstract: In this article, a pair of wavelets for Hermite cubic spline bases are presented. These wavelets are in $C^{1} $C1 and supported on $[-1,1] $[−1,1]. These spline wavelets are then adapted to the interval $[0,1] $[0,1] and we prove that they form a Riesz wavelet in $L_2([0,1]) $L2([0,1]). The wavelet bases are used to solve the linear optimal control problems. The operational matrices of integration and product are then utilised to reduce the given optimisation problems to the system 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. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Date: 2020
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DOI: 10.1080/00207721.2020.1739356

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