5. Hybrid systems: Hybrid equations
Exercises
B(E)3M35HYS – Hybrid systems
0. Introduction
What is a hybrid system?
Course annotation and outline
Rules of the course
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1. Discrete-event systems: Automata
Learning goals
Discrete-event systems
State automata
Software
Literature
Exercises
2. Discrete-event systems: Petri nets
Learning goals
Petri nets
Timed Petri nets
Software
Literature
Exercises
3. Discrete-event systems: Max-plus systems
Learning goals
Max-plus algebra
Max-plus linear (MPL) systems
Software
Literature
Exercises
4. Hybrid systems: Hybrid automata
Learning goals
Hybrid automata
Software
Literature
Exercises
5. Hybrid systems: Hybrid equations
Learning goals
Hybrid equations
Software
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Exercises
6. Some classes of hybrid systems
Learning goals
Reset systems
Switched systems
Piecewise affine (PWA) systems
Software
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Exercises
7. Solution
Learning goals
Solution concepts
Types of solutions
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8. Stability I.
Learning goals
Recap of stability analysis for continuous dynamical systems
Stability of hybrid systems
Stability via common Lyapunov function
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9. Stability II.
Learning goals
Stability via multiple Lyapunov functions
Software
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10. Complementarity systems
Learning goals
Complementarity constraints
Complementarity systems
Simulations of complementarity systems using time-stepping
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11. Mixed logical dynamical (MLD) systems
Learning goals
Discrete hybrid automata
Logic vs inequalities
Components of DHA as inequalities
Mixed logical dynamical (MLD) systems
Software
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12. Model predictive control (MPC) for MLD systems
Learning goals
Online MPC for hybrid systems
Explicit MPC for hybrid systems
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13. Formal verification I.
Learning goals
What is verification?
Reachability analysis
Barrier certificates
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14. Formal verification II.
Learning goals
Temporal logics
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5. Hybrid systems: Hybrid equations
Exercises
Exercises
Exercise 1: xxx (≈45 min)
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