Course outline

The course is structured into 14 topics, each of them corresponding to one lecture. The topics are as follows:

• Discrete-event systems
  1. (State) automata (state machines) (incl. timed variants)
  2. Petri nets (and timed Petri nets),
  3. Max-Plus algebra and Max-Plus Linear (MPL) systems
• Hybrid systems
  4. Hybrid automata
  5. Hybrid equations
• Special classes of hybrid systems
  6. Reset (control) systems, Switched/switching systems, Piecewise affine systems (PWA)
  7. Complementarity dynamical systems (and complementarity optimization constraints)
     

8. Solutions of hybrid systems

• Stability of hybrid systems
  9. Common Lyapunov function
     • Quadratic Lyapunov function via linear matrix inequality (LMI) and semidefinite programming (SDP)
     • Polynomial Lyapunov function via sum-of-squares (SOS) programming
  10. Piecewise quadratic/polynomial Lyapunov function via S-procedure

11. Mixed-logical dynamical (MLD) description of hybrid systems
12. Model predictive control (MPC) for MLD systems
13. (Formal) verification of hybrid systems