# Recurrent Trainable Neural Network

## Model description:

The RTNN model is described bythe following equations:

$$\begin{align*} X(k+1) &= JX(k) + BU(k)\\ Z(k) &= S[X(k)]\\ Y(k) &= S[CZ(k)]\\ J &\doteq \mathrm{blockdiag}(J_i); |J_i| <1, \end{align*}$$

here $X(\cdot)$ is a $n$-state vector of the RTTN; $U(\cdot)$ is a $m$-input vector; $Y(\cdot)$ is a $l$-output vector; $Z(\cdot)$ is an auxiliary vector variable with $l$ dimension; $S(\cdot)$ is a vector-valued smooth activation function (sigmoid, $tanh$, saturation) with appropriate dimensions; $J$ is a weigh-state block-diagonal matrix with $(1 \times 1)$ and $(2 \times 2)$ blocks; $J_i$ is an $i-th$ block of $J$ and $|J_i|<1$ is a stability condition.

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## Publication details:

Title | Adaptive Neural Control of Nonlinear Systems |

Publication Type | Conference Paper |

Year of Publication | 2001 |

Authors | Garrido, Ruben |

Editor | Baruch, Ieroham, Flores Jose Martin, and Thomas Federico |

Conference Name | International Conference on Artificial Neural Networks - ICANN 2001 |

Date Published | 08/2001 |

Publisher | Springer |

Conference Location | Vienna, Austria |

ISBN Number | 3-540-42486-5 |

URL | http://dblp.uni-trier.de/rec/bib/conf/icann/2001 |