中文摘要：

使用勒让德正交多项式逼近方法,将Lagrange型最优控制问题转化为非线性规划问题.采用序列二次规划方法对此非线性规划问题的求解,并对多项式逼近和非线性规划求解后得到的解是否收敛给出了证明和实例分析.

英文摘要：

In this paper,using the Legendre orthogonal polynomial approximation method,Convert the optimal control of Lagrange type problems into nonlinear programming problem.Using sequential quadratic programming method to solve the nonlinear programming problem,the conclusion whether the solution convergence which is obtained from solve nonlinear programming is proved and the example is analyzed.