### Abstract

We have proposed a novel robust inversion-based neurocontroller that searches for the optimal control law by sampling from the estimated Gaussian distribution of the inverse plant model. However, for problems involving the prediction of continuous variables, a Gaussian model approximation provides only a very limited description of the properties of the inverse model. This is usually the case for problems in which the mapping to be learned is multi-valued or involves hysteritic transfer characteristics. This often arises in the solution of inverse plant models. In order to obtain a complete description of the inverse model, a more general multicomponent distributions must be modeled. In this paper we test whether our proposed sampling approach can be used when considering an arbitrary conditional probability distributions. These arbitrary distributions will be modeled by a mixture density network. Importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The effectiveness of the importance sampling from an arbitrary conditional probability distribution will be demonstrated using a simple single input single output static nonlinear system with hysteretic characteristics in the inverse plant model.

Original language | English |
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Title of host publication | Intelligent Control Systems and Signal Processing 2003 |

Subtitle of host publication | IPV-IFAC Proceedings |

Editors | António E. de Barros Ruano |

Publisher | Australian Academic Press |

Pages | 387-392 |

Number of pages | 6 |

Volume | 2 |

ISBN (Print) | 978-0-08044088-0 |

Publication status | Published - Apr 2003 |

Event | IFAC International Conference on Intelligent Control Systems and Signal Processing - Faro, Portugal Duration: 1 Apr 2003 → 1 Apr 2003 |

### Conference

Conference | IFAC International Conference on Intelligent Control Systems and Signal Processing |
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Abbreviated title | ICONS |

Country | Portugal |

City | Faro |

Period | 1/04/03 → 1/04/03 |

### Keywords

- inversion-based neurocontroller
- Gaussian distribution
- prediction of continuous variables
- Gaussian model approximation
- hysteritic transfer characteristics
- inverse plant models
- multicomponent distribution
- arbitrary conditional probability distributions
- sampling
- Neural Networks

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## Cite this

Herzallah, R., & Lowe, D. (2003). Multi-valued control problems and mixture density network. In A. E. de Barros Ruano (Ed.),

*Intelligent Control Systems and Signal Processing 2003: IPV-IFAC Proceedings*(Vol. 2, pp. 387-392). Australian Academic Press.