A Hermite‐Lobatto Pseudospectral Method for Optimal Control

摘要: A pseudospectral (PS) method based on Hermite interpolation and collocation at the Legendre-Gauss-Lobatto (LGL) points is presented for direct trajectory optimization costate estimation of optimal control problems. major characteristic this that state approximated by instead commonly used Lagrange interpolation. The derivatives its approximation terminal time are set to match up using a Since derivative determined from dynamic, can automatically satisfy dynamic time. When collocating LGL points, equation point be omitted because it constantly satisfied. By approach, proposed avoids issue Legendre PS where discrete variables over-constrained equations, hence achieving same level solution accuracy as Gauss Radau method, while retaining ability explicitly generate endpoints. mapping relationship between Karush-Kuhn-Tucker multipliers nonlinear programming problem developed method. numerical example illustrates use described leads produce both highly accurate primal dual solutions