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Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems
Received:2009/6/3  Revised:2009/11/12
Keywords:Computational optimal control  Pseudospectral method  Convergence
Fund Project:This work was partly supported by the Air Force Office of Scientific Research (No.F1ATA0-90-4-3G001) and Air Force Research Laboratory.
Wei KANG Department of Applied Mathematics, Naval Postgraduate School, Monterey CA 93943, USA wkang@nps.edu 
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      Pseudospectral (PS) computational methods for nonlinear constrained optimal control have been applied to many industrial-strength problems, notably, the recent zero-propellant-maneuvering of the international space station performed by NASA. In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using a Legendre PS method. In addition to the high-order convergence rate, two theorems are proved for the existence and convergence of the approximate solutions. Relative to existing work on PS optimal control as well as some other direct computational methods, the proofs do not use necessary conditions of optimal control. Furthermore, we do not make coercivity type of assumptions. As a result, the theory does not require the local uniqueness of optimal solutions. In addition, a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems is removed.
Wei KANG.Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems[J].Journal of Control Theory and Applications,2010,8(4):391~405.
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