On realizability of neural networks-based input–output models in the classical state-space form

Automatica ◽  
2006 ◽  
Vol 42 (7) ◽  
pp. 1211-1216 ◽  
Author(s):  
Ü. Kotta ◽  
F.N. Chowdhury ◽  
S. Nõmm
Keyword(s):  
Neural Networks ◽  
State Space ◽  
Space Form ◽  
Input Output ◽  
Classical State

TRANSFER EQUIVALENCE AND REALIZATION OF NONLINEAR HIGHER ORDER INPUT/OUTPUT DIFFERENCE EQUATIONS USING MATHEMATICA

1999 ◽  
Vol 09 (01n02) ◽  
pp. 23-35 ◽  
Author(s):  
ÜLLE KOTTA ◽  
MARIS TÕNSO
Keyword(s):  
Control Systems ◽  
Difference Equations ◽  
Space Form ◽  
Higher Order ◽  
Nonlinear Control Systems ◽  
Input Output ◽  
Nonlinear Case ◽  
State Equations ◽  
Order Difference ◽  
Classical State

This paper presents a contribution to the development of symbolic computation tools for discrete-time nonlinear control systems. A set of functions is developed in Mathematica 3.0 that test if the higher order input/output difference equation is realizable in the classical state-space form, and for simple examples, also find such state equations. The approach relies on a new notion of equivalence of higher order difference equations which yields a minimal (i.e. accessible and observable) realization and generalizes the notion of transfer equivalence to the nonlinear case. The application of the developed functions is demonstrated on three examples obtained via identification.

scholarly journals ON CLASSICAL STATE SPACE REALIZABILITY OF QUADRATIC INPUT-OUTPUT DIFFERENTIAL EQUATIONS

2007 ◽  
Vol 40 (20) ◽  
pp. 332-337
Author(s):  
ü. Kotta ◽  
P. Kotta ◽  
M. Tõnso ◽  
A.S.I. Zinober
Keyword(s):  
Differential Equations ◽  
State Space ◽  
Input Output ◽  
Classical State

Classical state space realizability of input-output bilinear models

2003 ◽  
Vol 76 (12) ◽  
pp. 1224-1232 ◽  
Author(s):  
Ü. Kotta ◽  
S. Nõmm ◽  
A. S. I. Zinober
Keyword(s):  
State Space ◽  
Input Output ◽  
Classical State ◽  
Bilinear Models

On classical state space realisability of quadratic input–output differential equations

2009 ◽  
Vol 82 (7) ◽  
pp. 1212-1218 ◽  
Author(s):  
Ü. Kotta ◽  
P. Kotta ◽  
M. Tõnso ◽  
A.S.I. Zinober
Keyword(s):  
Differential Equations ◽  
State Space ◽  
Input Output ◽  
Classical State

Minimal realisation of bilinear and quadratic input–output difference equations in state-space form

2011 ◽  
Vol 84 (12) ◽  
pp. 2024-2034 ◽  
Author(s):  
J. Belikov ◽  
P. Kotta ◽  
Ü. Kotta ◽  
A.S.I. Zinober
Keyword(s):  
State Space ◽  
Difference Equations ◽  
Space Form ◽  
Input Output

Parametrizations of All Wavelet Filters: Input-Output and State-Space

2013 ◽  
Vol 12 (2-3) ◽  
pp. 159-188
Author(s):  
Daniel Alpay ◽  
Palle Jorgensen ◽  
Izchak Lewkowicz
Keyword(s):  
State Space ◽  
Input Output ◽  
Wavelet Filters

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

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