Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Dinamics and optimization of engineering sistems (17.MIT009)

Type of studies	Title
Undergraduate Academic Studies	Technical Mechanics and Technical Design (Year: 4, Semester: Summer)

General information:

Category	Scientific-professional
Scientific or art field	Mechanics
ECTS	6

To introduce students to the basic optimization methods and their practical applications to problems posed within mechanical systems. To extend previously analyzed models to new ones including distributions, differential equations with piecewise continuous right hand side, and memory effects by use of fractional derivatives; to apply nonsmooth analysis in problem posing and problem solving, dealing with motion in the presence of collisions and dry friction

Knowledge acquisition from the field of variational calculus and optimal control for dynamical systems and ability to use these tools in solving a variety of problems in structural and process design within mechanics and engineering in order to optimize the values of selected physical parameters. Ability to predict different motion scripts by use of models given in form of integro-differential inclusion; understanding and usage of notions belonging to non-smooth analysis and fractional calculus in the framework of problem posing and problem solving.

This course covers the following topics. Elements of variational calculus. Hamilton principle. variational problems with constraints. Variational calculus in terms of canonical variables with applications in mechanics. Optimal control problem by means of variational calculus. Constrained optimal problems. The maximum principle of Pontryagin. Applications in motion control and structural design. The Belman dynamical programming theory in discrete and continuous multistage processes. Elements of nonsmooth - nonconvex optimization. Examples. The derivative in sense of distributions and distributional model of external collision. The generalized Euler-Lagrange equations. Internal collision and impact theories of the Hertz type - approximative models. Energy dissipation during impacts. The Kelvin-Zener model of viscoelastic body. Fractional derivative and the fractional Kelvin-Zener model of viscoelastic body. Restrictions on the rheological model that follow from the Clausius-Duhem inequality. The Mittag-Leffler function and the Laplace transform of the left Riemann-Liouville fractional derivative. The Post inversion formula. Simple deformation pattern and parameter identification based on rheological experiments. The Post-Newton method. Dry friction force models. Multifunctions (set-valued functions) and the Coulomb dry friction model. Dual nature of friction force in mechanics. Dual nature of friction force in mathematics. Differential inclusions.

Lectures, auditory exercises, demonstration of computer tools. Homeworks, as a check of understanding and usage of the introduced notions that can be done within groups. Either a practical examination part -- two problems done by them own -- or seminar work based on a real problem presented in periodicals. Individual work with each of the groups which extends the knowledge and skills in analysis and formulation of an optimization problem as well its numerical solving. The examination ends with a final talk on the introduced notions and skills in solving optimization problems and problems dynamics of nonsmooth mechanical systems.

Authors	Title	Year	Publisher	Language
Bellman, R.	Introduction to the Mathematical Theory of Control Processes	1967	Academic Press, New York	English
Bryson, A.E., Ho, Y.C.	Applied Optimal Control	1975	John Wiley & Sons, New York	English
B. Brogliato	Nonsmooth mechanics	1999	Springer, London	English
Kirk, D.E.	Optimal Control Theory	1970	Prentice-Hall, New Jersey	English

Course activity	Pre-examination	Obligations	Number of points
Homework	Yes	Yes	5.00
Project	Yes	Yes	30.00
Homework	Yes	Yes	5.00
Practical part of the exam - tasks	No	Yes	30.00
Lecture attendance	Yes	Yes	5.00
Exercise attendance	Yes	Yes	5.00
Oral part of the exam	No	Yes	20.00