Mathematical Control Theory, 5 op

The course studies linear time-invariant dynamical systems described by ordinary and partial 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, observability, stabilization, and ”proportional-integral (PI) control”. The first half of the course focuses on control of finite-dimensional systems and the second half on control linear infinite-dimensional systems. Infinite-dimensional control systems are in particular used in the study of controlled partial differential equations, such as diffusion equations and wave equations, and their theory is based on functional analysis and operator theory.

The theoretical results of the course are illustrated with examples involving controlled ordinary and partial differential equations, especially controlled mechanical systems, groups of moving robots, as well as controlled heat, diffusion and vibration processes. Matlab is used to approximate and simulate the control systems.