On Integral Interpolation Error Analysis Based Pseudospectral Method with Application to Minimum Time-to-Climb Problem

This paper focuses on multistage pseudospectral method for solving optimal control problems by introducing a novel method of integral interpolation error analysis. Different from traditional studies that using the maximum error on the collocation points to judge the approximate effect, this paper considers the approximate error of integral interpolation in the entire time domain. It is shown that integral interpolation error between the solutions of continuous optimal problem and NLP problem can be bounded by a constructed definite integral which can be calculated online. More importantly, a new algorithm with tuning the number of intervals and the number of corresponding collocation points via the constructed definite integral is presented. The proposed algorithm is applied to solving minimum time-to-climb problem. The simulation results demonstrate that the proposed algorithm performs well by finding the well-suited parameters.