| Optimizare şi control optimal | Optimization and optimal control |
trul |
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(Applied Mathematics) |
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(Mathematics Economics) |
| Cadre didactice indrumatoare | Teaching Staff in Charge |
| Prof. Dr. MURESAN Marian, mmarian@math.ubbcluj.ro |
| Obiective | Aims |
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Familiarizarea studentilor cu problemele de calcul variational si control optimal: recunoasterea lor, formularea lor intr-un limbaj matematic, folosirea unor metode pentru gasirea si studiul solutiilor. |
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. |
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1. Introducere
1.1. Calcul variational. Probleme si formularea lor matematica 1.2. Control optimal. Probleme si formularea lor matematica 2. Calcul variational 2.1. Conditii necesare: ecuatia Euler-Lagrange, conditiile lui Weierstrass, Legendre, Erdman si Jacobi; conditii cu derivata Gateaux, conditia de transversalitate 2.2. Teorema de existenta a lui Tonelli 2.3. Conditii suficiente de tip Weierstrass si de tip Hamilton-Jacobi 3. Controlul optimal al sistemelor liniare si liniar-patratice 3.1. Teorema bang-bang 3.2. Controlabilitate si observabilitate pentru ecuatii si incluziuni diferentiale. 3.3. Principiul maximului. Diferite forme. 3.4. Sinteza 3.5. Dualitate 4. Aplicatii in economie si inginerie |
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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. |
| Evaluare | Assessment |
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Un referat si un examen oral |
A review and an exam. |