Multi-objective stochastic design of robust PI controllers for systems with probabilistic uncertainty using genetic algorithm.

*(English)*Zbl 1157.93453
Gammerman, A. (ed.), Artificial intelligence and applications. Machine learning. As part of the 26th IASTED international multi-conference on applied informatics. Calgary: International Association of Science and Technology for Development (IASTED); Anaheim, CA: Acta Press (ISBN 978-0-88986-710-9/CD-ROM). 290-295 (2008).

Summary: A robust approach for the Pareto optimum design of PI controllers for systems with probabilistic uncertainty is
presented. In this way, some non-dominated optimum PI controllers in the Pareto sense are found using three noncommensurable objective functions both in time and frequency domains based on stochastic behaviour of a system with parametric uncertainties. Such conflicting objective functions are, namely, the probability of instability, the probability of failure to a desired time response and its variance, and the degree of stability from the Nyquist diagram’s percentiles. The first two objective functions have to be minimized whilst the last one to be maximized simultaneously. It is shown that multiobjective Pareto optimization of such robust PI controllers using a recently developed diversity preserving mechanism genetic algorithm unveils some very important and informative trade-offs among these objective functions. Consequently, some optimum PI controllers can be compromised and chosen from the Pareto frontiers.

For the entire collection see [Zbl 1154.68012].

For the entire collection see [Zbl 1154.68012].

##### MSC:

93C95 | Application models in control theory |

90B25 | Reliability, availability, maintenance, inspection in operations research |

68T05 | Learning and adaptive systems in artificial intelligence |

93E99 | Stochastic systems and control |

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\textit{N. Nariman-Zadeh} et al., in: Artificial intelligence and applications. Machine learning. As part of the 26th IASTED international multi-conference on applied informatics. Calgary: International Association of Science and Technology for Development (IASTED); Anaheim, CA: Acta Press. 290--295 (2008; Zbl 1157.93453)