### Abstract

In this paper, we propose a new method for constructing approximate value functions for nonlinear optimal regulator problems with infinite time horizons. We consider a canonical quantization, which is an operation to change classical mass systems to quantum mass systems. First, we apply the canonical quantization to mass systems equivalent to the optimal regulator systems. Second, we construct approximate optimal regulators by using the canonical quantized mass systems. Third, we clarify the conditions under which approximate solutions converge to the strict solutions. In addition, we demonstrate some examples with one-dimensional systems.

Original language | English |
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Title of host publication | Proceedings of the 18th IFAC World Congress |

Publisher | IFAC Secretariat |

Pages | 8058-8063 |

Number of pages | 6 |

Edition | 1 PART 1 |

ISBN (Print) | 9783902661937 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Number | 1 PART 1 |

Volume | 44 |

ISSN (Print) | 1474-6670 |

### Keywords

- Maximum principle
- Nonlinear control systems
- Optimal regulators

### Cite this

*Proceedings of the 18th IFAC World Congress*(1 PART 1 ed., pp. 8058-8063). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 44, No. 1 PART 1). IFAC Secretariat. https://doi.org/10.3182/20110828-6-IT-1002.01782