"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Optimization and optimal control
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MO040
8
2+2+0
8
optional
Matematica Economica
MO040
8
2+2+0
8
optional
Matematici Aplicate
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.