MMA1006 | Control optimal |
Titularii de disciplina |
Prof. Dr. MURESAN Marian, mmarianmath.ubbcluj.ro |
Obiective |
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. |
Continutul |
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. Fenomenul Lavrentiev 2.4. 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. Teorema lui Kalman 3.3. Principiul maximului 3.4. Sinteza 3.5. Dualitate 4. Aplicatii in economie si inginerie |
Bibliografie |
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. 6. Muresan, M., Introducere in control optimal, Risoprint, Cluj-Napoca, 1999. 7. Muresan, M. A Concret Approach to Classical Analysis, Springer, New York, 2008. 8. Vinter, R. B., Optimal Control, Notes, 75p. |
Evaluare |
Examen scris si oral. |
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