## Model description:

Consider the following unknown discrete nonlinear dynamic system:

$$\begin{align*} y(k+1)&=p[{\bf q}(k), u(k)]=0.2\cos[0.8(y(k)+y(k-1))] \\ & +0.4\sin[0.8(y(k)+y(k-1))+2u(k)+u(k-1)] \\ &+0.1[9+y(k)+y(k-1)]+\left[{2(u(k)+u(k-1))\over 1+\cos(y(k))}\right] \end{align*}$$

for $k=0,1,2,\ldots$ with $y(k)=0,u(k)=0$, for $k=0,-1,-2,\ldots$, $\Delta t := t(k+1)-t(k)=0.02sec$, for $k=0,1,2,\ldots$.

## Type:

## Form:

## Model order:

2

## Time domain:

## Linearity:

## Publication details:

Title | Robust nonlinear adaptive control using neural networks |

Publication Type | Conference Paper |

Year of Publication | 2001 |

Authors | Adetona, O., Sathananthan S., and Keel L.H. |

Conference Name | Proceedings of the 2001 American Control Conference, 2001 |

Date Published | 06/2001 |

Publisher | IEEE |

Conference Location | Arlington, VA |

ISBN Number | 0-7803-6495-3 |

Accession Number | 7092721 |

Keywords | adaptive control, asymptotic stability, neurocontrollers, nonlinear control systems, radial basis function networks, robust control |

Abstract | This paper provides a robust indirect adaptive control method for non-affine plants. Subject to some mild assumptions, the method can be applied to both minimum and non-minimum phase plants with operating regions of any finite size while avoiding a set of restrictions, at least one of which is imposed by all existing methods. The benefits are achieved under the following assumptions: 1) the operating region is limited to the basin of attraction of an asymptotically stable equilibrium point of the plant; 2) the desired output of the plant is sufficiently slowly varying; and 3) the output of the plant must be sufficiently sensitive to the input signal. It is shown that the adaptive control system will be stable in the presence of unknown bounded modeling errors |

DOI | 10.1109/ACC.2001.946247 |