Paper Info
Title
A unified framework for the numerical solution of optimal control problems using pseudospectral methods
Abstract
A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre–Gauss (LG), Legendre–Gauss–Radau (LGR), and Legendre–Gauss–Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme.
Year
DOI
Venue
2010
10.1016/j.automatica.2010.06.048
Automatica
Keywords
Field
DocType
Optimal control,Pseudospectral methods,Nonlinear programming
Rank (linear algebra),Mathematical optimization,Optimal control,Lagrange multiplier,Control theory,Matrix (mathematics),Square matrix,Gauss pseudospectral method,Discrete system,Mathematics,Collocation
Journal
Volume
Issue
ISSN
46
11
0005-1098
Citations 
PageRank 
References 
57
3.77
6
Authors
6
Name
Order
Citations
PageRank
Divya Garg11168.87
Michael Patterson2573.77
William W. Hager31603214.67
Anil V. Rao434129.35
David A. Benson516213.23
Geoffrey T. Huntington620115.92