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Stationary policies for lower bounds on the minimum average cost of discrete‐time nonlinear control systems
Author(s) -
Vargas Alessandro N.,
Ishihara João Y.,
Val João B.R.
Publication year - 2013
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.3034
Subject(s) - nonlinear system , control theory (sociology) , convergence (economics) , testbed , optimal control , state (computer science) , discrete time and continuous time , control (management) , algebraic number , computer science , nonlinear control , mathematical optimization , mathematics , algorithm , computer network , mathematical analysis , statistics , physics , quantum mechanics , artificial intelligence , economics , economic growth
SUMMARY The paper deals with the control problem of discrete‐time nonlinear systems. The main contribution of this note is to present conditions that assure the existence of stationary policies that generate lower bounds for the minimal long‐run average cost. These lower bounds coincide with the optimal solution when a mild convergence assumption holds. To illustrate the results, the paper presents an application for the simultaneous state‐feedback control problem, and the derived strategy is used to design a real‐time simultaneous control for two direct current motor devices. The dynamics of these two devices are written in terms of a nonlinear algebraic matrix recurrence, which in turn represents a particular case for our general nonlinear approach. The optimal gain for the corresponding simultaneous state‐feedback problem is obtained, and such a gain was implemented in a laboratory testbed to control simultaneously the two direct current motors. Copyright © 2013 John Wiley & Sons, Ltd.