To introduce students to the mathematical theory of optimal control and allow students to solve problems of optimal control of mechanical systems.

Upon successful completion of this course, students will be able to formulate the problem of optimal control of mechanical systems with finite number of degrees of freedom and to resolve it, including numerical solution of systems whose movement is described by nonlinear differential equations of motion.

Classic extremal problems in mechanics. Control in mechanical systems. The goal of motion control. Objective function. Optimal control. The differential equations of controlled mechanical system. Maximum principle. Transversality conditions. Limited control. Mechanical systems wuth limited phase state. Singular control. Examples of singular control. Parameter optimization. Motion control of rigid bodies. Examples of optimal control of rigid body systems motion. Optimal stabilization of motion of the mechanical system. Bellman optimality principle and the method of Lyapunov functions. Asymptotic stabilization of movement.

-

None

Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F., Mathematical Theory of Optimal Processes (in Russian). Nauka, Moscow, 1983. Vujanović B.D. and Spasić D.T. : Part II: Fundamentals of Optimal Control Theory", Novi Sad University Press, Novi Sad,2009.

Total assigned hours: 65

New material: 50
Elaboration and examples (recapitulation): 0

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 10
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 50

Fempl S., Elementi varijacionog računa, Građevinska knjiga, Beograd, 1965.; Hull DG, Optimal Control Theory for Applications, Springer, New York,2003.; Subchan S, Zbikowski R, Computational Optimal Control, Tools and Practice, WILEY, UK, 2009.; Leitmann G., An Introduction to Optimal Control, McGraw-Hill , New York,1966.; Sage P, White C , Optimum Systems Control. Prentice-Hall, Englewood, 1977.