### Abstract

A direct numerical method for optimal feedback control design of general nonlinear systems is presented in this chapter. The problem is generally infinite dimensional. In order to convert it to a finite dimensional optimization problem, a collocation type method is proposed. The collocation approach is based on approximating the control input function as a series of given base functions with unknown coefficients. Then, the optimal control problem is converted to the problem of finding a finite set of coefficients. To solve the resulting optimization problem, a new nature-inspired optimization paradigm known as Moth Flame Optimizer (MFO) is used. Validation and evaluating of accuracy of the method are performed via implementing it on some well known benchmark problems. Investigations presented in this chapter reveals the efficiency of the method and its benefits with respect to other numerical approaches. The chapter also consideres an in-depth literratur review and analysis of MFO.

Original language | English |
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Title of host publication | Studies in Computational Intelligence |

Publisher | Springer Verlag |

Pages | 143-166 |

Number of pages | 24 |

DOIs | |

Publication status | Published - 1 Jan 2020 |

Externally published | Yes |

### Publication series

Name | Studies in Computational Intelligence |
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Volume | 811 |

ISSN (Print) | 1860-949X |

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## Cite this

*Studies in Computational Intelligence*(pp. 143-166). (Studies in Computational Intelligence; Vol. 811). Springer Verlag. https://doi.org/10.1007/978-3-030-12127-3_9