Pseudospectral optimal control

Summary

Pseudospectral optimal control is a form of direct collocation that uses a single global polynomial for the state on the whole time interval. The nodes are the points of a Gaussian quadrature rule, such as the Legendre–Gauss–Lobatto points, and derivatives are taken with a differentiation matrix. For smooth problems the error decreases faster than any power of the number of nodes, so few nodes give high accuracy. The method is used in aerospace guidance, for example to plan spacecraft manoeuvres.