Research on the time precise computation of the nonlinear optimal control system

For the nonlinear optimal control problem, by taking the first term of the Taylor series, the dynamic equation is linearized. Thus by introducing into the dual variables (Lagrange multiplier vectors), the dynamic equation can be transformed into the Hamilton system from the Lagrange system on the basis of the original variable. Under the whole state, the problem in the paper can be described from a new view, and its equation can be precisely solved by the precise time integration method established in the linear dynamic system. A numerical example shows the effectiveness of the method.