Control Theory 1000-135TST
It is an introduction to modern mathematical Control Theory. The theory is illustrated by numerous examples from economy, biology, medicine, physics and technology. In particular: controllability for linear and nonlinear systems, bang-bang principle, time-optimal control, Pontriagin Maximum Principle, transversality, dynamic programming.
Main fields of studies for MISMaP
Course coordinators
Type of course
Mode
Prerequisites (description)
Learning outcomes
Students:
1. Know what is a control problem and in particular a linear control problem;
2. Know basic theorems related to controllability of linear control problems;
3. Know what are reachable sets;
4. Know basic theorems related to controllability of non-linear control problems;
5. Know the bang-bang principle;
6. Know the time optimal control problems;
7. Know the the Pontryagin Maximum Principle for linear time optimal control problems;
8. Know theorems on existence of solutions for optimal control problems;
9. Know how to state and use the Pontryagin Maximum Principle;
10. Know the transversality conditions;
11. Know how to apply the methods of the control theory to simple examples from economy, biology, medicine, physics and engineering
Social competence:
Students understands the role of the control theory as a tool for understanding the laws of Nature
Assessment criteria
exam
Bibliography
E.D. Sontag, Mathematical Control Theory. II edition, Springer, New York 1998, available in internet.
L.C. Evans, An Introduction to Mathematical Optimal Control Theory, available in internet.