ABSTRACT In this article, a pair of wavelets for Hermite cubic spline bases are presented. These wavelets are in and supported on . These spline wavelets are then adapted to the interval and we prove that they form a Riesz wavelet in . 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.

中文翻译：

---

用于离散化约束最优控制问题的导数正交小波

摘要 在本文中，介绍了 Hermite 三次样条基的一对小波。这些小波在 . 然后将这些样条小波适应于区间，我们证明它们在 中形成 Riesz 小波。小波基用于解决线性最优控制问题。然后利用积分和乘积的运算矩阵将给定的优化问题简化为代数方程组。由于这些矩阵的稀疏性，这种方法在计算上非常有吸引力，并减少了 CPU 时间和计算机内存。为了节省内存要求和计算时间，应用阈值程序来获得代数方程。包括说明性示例以证明该技术的有效性和适用性。