In this paper, a new orthonormal wavelets based on the sixth-kind Chebyshev polynomials is constructed to obtain the solution of fractional optimal control problems (FOCPs) with inequality constraints. The convergence analysis and error estimate of the sixth-kind Chebyshev wavelets function expansion are investigated. By using the relationship between the second-kind and sixth-kind Chebyshev polynomials, the exact formula of Riemann-Liouville fractional integral operator of Chebyshev wavelet is derived. For solving FOCPs, positive slack functions are added to inequality conditions, and then the problem is simplified to the problem of solving algebraic equations by fractional integral operational matrix and collocation method. The applicability and validity of the proposed method are verified by several examples and the results are compared with those reported in literature.

本文构造了一个基于第六类切比雪夫多项式的新的正交小波来求解具有不等式约束的分数最优控制问题(FOCPs)。研究了第六类切比雪夫小波函数展开的收敛性分析和误差估计。利用第二类和第六类切比雪夫多项式之间的关系，推导出了切比雪夫小波的黎曼-刘维尔分数积分算子的精确公式。求解FOCPs，在不等式条件中加入正松弛函数，然后将问题简化为用分数积分运算矩阵和搭配方法求解代数方程的问题。