NLq Theory

  • Johan A. K. Suykens
  • Joos P. L. Vandewalle
  • Bart L. R. De Moor
Chapter

Abstract

In this Chapter we develop a model based neural control framework which consists of neural state space models and neural state space controllers. Like in modern (robust) control theory standard plant forms are considered. In order to analyse and synthesize neural controllers within this framework, the so-called NL q system form is introduced. NL q s represent a large class of nonlinear dynamical systems in state space form and contain a number of q layers of an alternating sequence of linear and static nonlinear operators that satisfy a sector condition. All system descriptions are transformed into this NL q form and sufficient conditions for global asymptotic stability, input/output stability with finite L2-gain and robust performance are derived. It turns out that NL q s have a unifying nature, in the sense that many problems arising in neural networks, systems and control can be considered as special cases. Moreover, certain results in H and μ control theory can be interpreted as special cases of NL q theory. Examples show that following principles from NL q theory, stabilization and control of several types of nonlinear systems are possible, including mastering chaos.

Keywords

Closed Loop System Cellular Neural Network Global Asymptotic Stability Neural Controller Diagonal Dominance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Johan A. K. Suykens
    • 1
  • Joos P. L. Vandewalle
    • 1
  • Bart L. R. De Moor
    • 1
  1. 1.K.U. LeuvenBelgium

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