Mathematical Control Theory, 5 op

The course studies linear time-invariant dynamical systems described by linear and nonlinear differential equations from the time-domain and frequency-domain points of view. The course presents a mathematical introduction to the fundamental concepts of control theory, including controllability, stability, stabilization, and ”proportional-integral (PI) control”. The first half of the course focuses on control of linear systems and the second half on control nonlinear systems. Nonlinear analysis is especially used in the study of dynamical properties of the nonlinear pendulum model and in control design for stabilization and output tracking of systems with nonlinear dynamics.

The theoretical results of the course are illustrated with examples involving controlled linear and nonlinear differential equations, especially controlled mechanical systems, groups of moving robots, as well linear systems with input nonlinearities. Matlab is used to approximate and simulate the control systems.