Improved Gauss Pseudospectral Method For a Class of Optimal Control Problems

An improved Gauss pseudospectral (IGP) method is proposed to solve the Bolza optimal control problem in this paper. Firstly any definition interval of the Bolza optimal control problem can be mapped to [-1,1] by the IGP method, secondly the objective function is discretized into a constrained nonlinear programming problem, then equivalently convert the terminal state variables into a linear form, finally the new costate mapping theorem of the IGP method is proved, which shows that the nonlinear programming problem transformed by IGP method is equivalent to the first-order necessary condition of the Bolza problem.