Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMA1006 | Optimal Control Theory |
| Teaching Staff in Charge |
Prof. MURESAN Marian, Ph.D., mmarian math.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 |
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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 |
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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. 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 |
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Written and oral exam. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |