Gauss Pseudospectral Method, GPM

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A direct method for solving optimal control problems. It discretizes the continuous optimal control problem into a nonlinear programming (NLP) problem using Legendre-Gauss collocation points. Dynamics constraints depend only on the current node state, keeping the parameter space small. The KKT conditions at collocation points are equivalent to the first-order optimality conditions of the Pontryagin maximum principle, yielding high accuracy. It inherits the exponential convergence property of pseudospectral methods.

Application Value

The Gauss伪谱法 concept is applied in cislunar space research, providing technical support or analytical methods for lunar exploration missions.

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References

  • 平动点周期轨道间小推力转移的Gauss伪谱法