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Theory and application of Legendre pseudo-spectral method for solving optimal control problems. (Chinese. English summary) Zbl 1324.49028

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.

MSC:

49M37 Numerical methods based on nonlinear programming
90C30 Nonlinear programming

Software:

PoPS; Matlab
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