DocumentCode :
3565844
Title :
Uniform approximation of discrete-time nonlinear systems
Author :
Ciraula, Michael ; Sandberg, Irwin W.
Author_Institution :
IBM Corp., Austin, TX, USA
Volume :
1
fYear :
1999
fDate :
6/21/1905 12:00:00 AM
Firstpage :
611
Abstract :
We consider a large class of discrete-time control systems containing a dynamic linear part and a memoryless nonlinear element and show that such systems can be uniformly approximated using a TDNN, a two-stage dynamic neural structure consisting of a bank of delay elements followed by a memoryless nonlinear element. In addition, we bound the complexity of the TDNN needed to uniformly approximate the system to within a given maximum error ε. Specifically, we bound the number of delay elements a by giving constants ρ1 and ρ2 such that α>ρ1 log(ρ2 /ε) suffices, and we show that the nonlinear element satisfies a certain Lipschitz condition. Our assumptions are along the lines of the circle condition for stability, and the concept of approximately finite memory plays a central role in our results
Keywords :
approximation theory; discrete time systems; feedback; neural nets; nonlinear systems; stability criteria; Lipschitz condition; circle condition; delay elements; discrete-time systems; feedback; memoryless nonlinear element; neural nets; nonlinear systems; stability; uniform approximation; Control systems; Delay effects; Ear; Neurofeedback; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Polynomials; Stability; USA Councils;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Neural Networks, 1999. IJCNN '99. International Joint Conference on
ISSN :
1098-7576
Print_ISBN :
0-7803-5529-6
Type :
conf
DOI :
10.1109/IJCNN.1999.831568
Filename :
831568
Link To Document :
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