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On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems
Author(s) -
Kang W.,
Gong Q.,
Ross I. M.,
Fahroo F.
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1166
Subject(s) - pseudospectral optimal control , optimal control , convergence (economics) , nonlinear system , control theory (sociology) , discontinuity (linguistics) , pseudo spectral method , gauss pseudospectral method , mathematics , controller (irrigation) , generalization , nonlinear control , sequence (biology) , mathematical optimization , computer science , control (management) , mathematical analysis , fourier analysis , physics , genetics , fourier transform , quantum mechanics , artificial intelligence , agronomy , economics , biology , economic growth
We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. In contrast to the existing results, the optimal controller addressed in this paper is allowed to be discontinuous. This generalization requires a substantial modification to the existing convergence analysis in terms of both the framework as well as the notion of convergence around points of discontinuity. Although the nonlinear system is assumed to be feedback linearizable, the optimal control does not necessarily linearize the dynamics. Such problems frequently arise in astronautical applications where stringent performance requirements demand optimality over feedback linearizing controls. We prove that a sequence of solutions obtained using the Legendre pseudospectral method converges to the optimal solution of the continuous‐time problem under mild conditions. Published in 2007 by John Wiley & Sons, Ltd.