The Legendre pseudospectral method for optimal control

Optimal control

Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...

 problems is based on Legendre polynomials. It is part of the larger pseudospectral optimal control

Pseudospectral optimal control

Pseudospectral optimal control is a computational method for solving optimal control problems. Pseudospectral optimal control techniques have been extensively used to solve a wide range of problems such as those arising in UAV trajectory generation, missile guidance, control of robotic arms,...

 theory, that was originally proposed by Elnagar and coworkers in 1995. Since then, Ross, Fahroo and co-workers have analysed, extended and applied the method for an impressive range of problems. An application that has received wide publicity is the use of their method for generating real time trajectories for the International Space Station

International Space Station

The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...

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Software

The method was first implemented in DIDO

DIDO (optimal control)

DIDO is a MATLAB program for solving hybrid optimal control problems. Powered by the pseudospectral knotting method, the general-purpose program is named after Dido, the legendary founder and first queen of Carthage who is famous in mathematics for her remarkable solution to a constrained optimal...

in 2001. Today, it is also available in other software packages such as OTIS and PSOPT.