hybrid_system_course_mindmap.md

B(E)3M35HyS

Discrete-event systems

1. (State) automata (state machines) (and timed automata)
2. Petri nets (and timed Petri nets),
3. Max-Plus algebra and Max-Plus Linear (MPL) systems

Modelling hybrid systems

4. Hybrid automata
5. Hybrid equations

6. Special classes of hybrid systems

• Reset (control) systems
• Switched/switching systems
• Piecewise affine systems (PWA)

7. Numerical simulation of hybrid systems

• Complementarity dynamical systems (and complementarity optimization constraints)

Analysis of hybrid systems

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 / Putinar's Positivstellensatz

Control design

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

13. Verification of hybrid systems

• Reachability analysis
  • (In)feasibility of an optimal control problem
  • Set propagation techniques
• (Control) barrier functions
• Temporal logics
  • LTL, CTL, CTL*, MTL, MITL, TCTL*, STL, ...