Solving fractional optimal control problems with inequality constraints by a new kind of Chebyshev wavelets method

摘要

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 RiemannLiouville 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.