Hybrid Systems

1. Discrete Event Systems and Petri Nets
   1. Introduction to Discrete Event Systems
   2. Petri Nets (PNs): PN Graphs; PN Marking; PN dynamics.
   3. Special classes of PNs: Event Graphs and State Machines.
   4. Analysis of Petri Net Models: PN Properties and the Coverability Tree.
   5. Control of Petri Net Models: state-based control for the ideal case and for unobservable/uncontrollable transitions.
   6. Timed Petri Nets: timing mechanisms and timed event graphs.
2. Max Plus Algebra
   1. Introductory Example
   2. Max-plus algebra as an idempotent semiring
   3. Max-plus algebra and precedence graph properties
   4. Linear equations in max-plus
   5. The max-plus eigenvalue problem
   6. Industrial example: the control of high-throughput-screening
      (HTS) plants
3. Finite State Machines and Regular Languages
4. Supervisory Control Theory
   1. Modelling the plant
   2. Formal specifications
   3. Minimal restrictive control
   4. Controller realisation
5. Comparing Finite State Machines and Petri Nets
6. Introduction to Hybrid Systems
7. Hybrid Automata
8. Abstraction-based Control of Hybrid Systems
   1. Important abstraction properties
   2. l-complete approximation
   3. Handling complexity
9. Optimal Trajectories for Hybrid Automata
10. Stability of Switched Systems
    1. Stability concepts
    2. Stability under arbitrary switching
    3. Stability under state-dependent switching