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Short communication: A collocation‐type method for linear quadratic optimal control problems
Author(s) -
ELNAGAR GAMAL N.,
RAZZAGHI MOHSEN
Publication year - 1997
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199705/06)18:3<227::aid-oca598>3.0.co;2-a
Subject(s) - mathematics , optimal control , linear quadratic gaussian control , collocation (remote sensing) , gauss , polynomial , quadratic equation , quadratic programming , mathematical optimization , state (computer science) , computer science , algorithm , mathematical analysis , physics , geometry , quantum mechanics , machine learning
This communication presents a spectral method for solving time‐varying linear quadratic optimal control problems. Legendre–Gauss–Lobatto nodes are used to construct the m th‐degree polynomial approximation of the state and control variables. The derivative x ·( t ) of the state vector x ( t ) is approximaed by the analytic derivative of the corresponding interpolating polynomial. The performance index approximation is based on Gauss–Lobatto integration. The optimal control problem is then transformed into a linear programming problem. The proposed technique is easy to implement, efficient and yields accurate results. Numerical examples are included and a comparison is made with an existing result.