Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master

SUBJECT

Code
Subject
MMA1006 Optimal Control Theory
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
3
2+2+0
speciality
optional
Teaching Staff in Charge
Prof. MURESAN Marian, Ph.D.,  mmarianmath.ubbcluj.ro
Aims
Introducing students to the field of variational calculus and optimal control: formulating a problem on variational calculus and optimal control, its study and solving.
Content
1. Introduction
1.1. Variational calculus. Problems and mathematical framework.
1.2. Optimal control. Problems and mathematical framework.
2. Variational calculus.
2.1. Necessary conditions: Euler-Lagrange equation, Weierstrass, Legendre, Erdman, and Jacobi conditions; conditions involving the Gateaux derivative, transversality condition.
2.2. The existence theorem of Tonelli.
2.3. Lavrentiev phenomenon.
2.4. Sufficiency conditions of Weierstrass and of Hamilton-Jacobi type.
3. Controlul optimal of linear systems and linear-quadratic systems.
3.1. Bang-bang theorems
3.2. Controlability and observability. Kalman theorem.
3.3. Maximum principle.
3.4. Synthesis.
3.5. Duality
4. Applications to economy and engeenering.
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.
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.
Assessment
Written and oral exam.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject