Time Precise Integration Method for Constrained Nonlinear Control System

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