Faculty of Mathematics and Computer Science

Optimization and optimal control |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Prof. MURESAN Marian, Ph.D., mmarian@math.ubbcluj.ro |

Aims |

Introducing the students into the world of variational calculus and optimal control theory problems: their recognition, their mathematical formulation, ability for finding and studing solutions. |

Content |

1. Introduction
1.1. Variational calculus. Problems and their formulation 1.2. Optimal control optimal. Problems and their formulation 2. Variational calculus 2.1. Necessary conditions: Euler-Lagrange, Weierstrass, Legendre, Erdman, and Jacobi conditions; conditions involving Gateaux derivative, and transversality condition 2.2. The existence theorem of Tonelli 2.3. Sufficient conditions of Weierstrass and of Hamilton-Jacobi kind 3. Controlul optimal 3.1. Bang-bang theorem 3.2. Controlability and observability for differential equations and inclusions 3.3. Maximum principle. Different forms 3.4. Sinthesis 3.5. Duality 4. Applications in economy and engeneering |

References |

1. Cesari, L., Optimization - Theory and Applications. Problems with Ordinary Differential Equations, Springer, New-York, 1983.
2. Clarke, F. H., Optimization and Nonsmooth Analysis, SIAM, Philadelphia, 1990. 3. Hestenes, M. R., Calculus of Variations and Optimal Control Theory, Wiley, New-York, 1966. 4. Lee, E. B., Markus, L., Foundations of Optimal Control Theory, Wiley, New-York, 1967. 5. Loewen, P. D., Optimal Control and Nonsmooth Analysis, AMS, Providence, 1993. |

Assessment |

A review and an exam. |