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SENSITIVITY APPROACH TO OPTIMAL CONTROL FOR AFFINE NONLINEAR DISCRETE‐TIME SYSTEMS
Author(s) -
Tang GongYou,
Xie Nan,
Liu Peng
Publication year - 2005
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2005.tb00408.x
Subject(s) - nonlinear system , optimal control , affine transformation , control theory (sociology) , sensitivity (control systems) , mathematics , discrete time and continuous time , series (stratigraphy) , convergence (economics) , sequence (biology) , rate of convergence , mathematical optimization , computer science , control (management) , key (lock) , engineering , paleontology , statistics , physics , genetics , computer security , quantum mechanics , artificial intelligence , electronic engineering , pure mathematics , economics , biology , economic growth
This paper deals with the optimal control problem for a class of affine nonlinear discrete‐time systems. By introducing a sensitivity parameter and expanding the system variables into a Maclaurin series around it, we transform the original optimal control problem for affine nonlinear discrete‐time systems into the optimal control problem for a sequence of linear discrete‐time systems. The optimal control law consists of an accurate linear term and a nonlinear compensating term, which is an infinite sequence of adjoint vectors. In the present approach, iteration is required only for the nonlinear compensation series. By intercepting a finite sum of the series, we obtain a suboptimal control law that reduces the complexity of the calculations. A numerical simulation shows that the algorithm can be easily implemented and has a fast convergence rate.