1996 Volume 116 Issue 7 Pages 849-857
This paper describes a new gradient method for some nonlinear optimal problems with unknown parameters and final time. The algorithm is developed by applying the viewpoint of gradient method. By introducing a false time variable and a new function vector that is defined from the derivative of constraint function with respect to false time variable, a set of differential equations about the partial derivative variables of this function can be derived. Based on the above partial derivatives, a modification rule of control output, a false time parameter and unknown parameters in system is presented. If the condition of the modification rule is satisfied, the value of cost funciton will monotonyly reach a minimum. According to the modification rule, a numerical calculation algorithm is developed. To verify the performance of the algorithm, two simulation examples are provided. By comparing the simulation result with the theoretical resolution, it is cleard that proposed algorithm can provide a correct and useful means for nonlinear optimal control problems.