Multiple-Interval Pseudospectral Method for Optimal Control Problem with Application to Trajectory Planning

In this paper, a class of optimal control problems with control input under constraints of multiple intervals is considered. The multiple interval pseudospectral based algorithm is proposed to obtain numerical solution. It is shown that the KKT conditions and continuous first order conditions are closely linked by discrete parameters. Moreover, we prove that the error between the discrete solution of NLP problem and continuous solution of an optimal control problem can be tuned by discrete parameters. The proposed method is applied to solve the typical aircraft trajectory planning problem. In order to conform to the actual operation instructions, the entire trajectory is divided into multiple intervals and control variables keep constant in every phase. The simulations demonstrate the effectiveness of proposed multiple-interval pseudospectral method.