Xu, Shaobing; Li, Shengbo; Cheng, Bo Theory and application of Legendre pseudo-spectral method for solving optimal control problems. (Chinese. English summary) Zbl 1324.49028 Control Decis. 29, No. 12, 2113-2120 (2014). Summary: The pseudo-spectral method approximates control and state variables through global interpolation polynomials, then converts the Optimal Control Problem (OCP) to a Nonlinear Programming Problem (NLP) effectively. It’s a kind of direct method with higher solving efficiency. The basic framework of the Legendre pseudo-spectral method converting the Bolza OCP into NLP is summarized, and the mapping between the costates of OCP and the KKT multiplier to NLP is derived. Furthermore, a numerical method is elaborated based on the quasi-Newton method in order to calculate the LGL collocation accurately. The multiphase strategy is also introduced for non-smooth systems. Finally, a universal optimal control solver POPS (pseudo-spectral optimal control problem solver) is developed based on the Legendre pseudo-spectral method in Matlab. Three typical optimal control problems are solved by using the solver POPS, and the results show the effectiveness of the proposed method and solver POPS. Cited in 2 Documents MSC: 49M37 Numerical methods based on nonlinear programming 90C30 Nonlinear programming Keywords:optimal control; pseudo-spectral method; nonlinear programming; numerical implementation Software:PoPS; Matlab PDFBibTeX XMLCite \textit{S. Xu} et al., Control Decis. 29, No. 12, 2113--2120 (2014; Zbl 1324.49028) Full Text: DOI