A numerical approach of optimal control for generalized delay systems by general legendre wavelets

A general Legendre wavelets approach is presented. The delay function is expanded by general Legendre wavelets. The general operational matrix of integration is introduced. By the general Legendre wavelets, the linear-quadratic problem of generalized delay systems are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples demonstrate that the algorithms are valid.