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**Delayed action control problems.**
*(English)*
Zbl 0203.47001

In this paper the optimal control problem of linear systems with time delays in both the state and control variables is considered. More specifically, systems which are modeled by linear functional differential equations are considered. The question of the existence of an optimal controller is studied, and the necessary and sufficient conditions for an optimal controller are derived. Also, systems with side constraints, multiple cost functionals or time varying delays are investigated.

Reviewer: D. H.. Chyung

### MSC:

49Kxx | Optimality conditions |

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\textit{D. H. Chyung} and \textit{E. B. Lee}, Automatica 6, 395--400 (1970; Zbl 0203.47001)

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### References:

[1] | Banks, H.T., Necessary conditions for control problems with variable lags, SIAM J. control, 6, (1968) · Zbl 0159.13002 |

[2] | Chyung, D.H.; Lee, E.B., Optimal systems with time delays, () · Zbl 0148.33804 |

[3] | Chyung, D.H.; Lee, E.B., Linear optimal systems with time delays, SIAM J. control, 4, 548-575, (1966) · Zbl 0148.33804 |

[4] | Chyung, D.H.; Lee, E.B., On certain extremal problems involving linear functional equation models, () · Zbl 0219.49008 |

[5] | Chyung, D.H., Optimal systems with multiple cost functionals, SIAM J. control, 5, 345-351, (1967) · Zbl 0153.12803 |

[6] | Halanay, A., () |

[7] | Kharatishvilli, G.L., The maximum principle in the theory of optimal processes with delay, Dokl. akad. nauk, SSSR, 136, 39-42, (1961) |

[8] | Kharatishvilli, G.L., A maximum principle in extremal problems with delays, () |

[9] | Lee, E.B., Geometric theory of linear controlled systems, () · Zbl 0176.39306 |

[10] | Lee, E.B., Variational problems for systems having delay in the control action, IEEE trans. aut. control, AC-13, 697-699, (1968) |

[11] | Lee, E.B.; Markus, L., () |

[12] | Pontryagin, L.S., () |

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