Universitatea "Babeş-Bolyai" din Cluj-Napoca

Facultatea de Matematică şi Informatică
FISA DISCIPLINEI

Optimizare şi control optimal Optimization and optimal control
Cod
Semes-
trul
Ore: C+S+L
Credite
Tipul
Sectia
MO040
8
2+2+0
8
optionala
Matematici Aplicate
(Applied Mathematics)
MO040
8
2+2+0
8
optionala
Matematica Economica
(Mathematics Economics)
Cadre didactice indrumatoare Teaching Staff in Charge
Prof. Dr. MURESAN Marian, mmarian@math.ubbcluj.ro
Obiective Aims
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.
Continut
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
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.
Evaluare Assessment
Un referat si un examen oral
A review and an exam.