Introduction to switched control systems
PART I – MODELING & SIMULATION
Formal models for hybrid systems:
- Finite automata
- Differential equations
- Hybrid automata
- Open hybrid automaton
Nondeterministic vs. stochastic systems:
- Nondeterministic hybrid automata
- Stochastic hybrid automata
Trajectories of hybrid system:
- Solution to an hybrid system
- Execution of an hybrid system
Degeneracies:
- Finite-escape time
- Chattering
- Zeno trajectories
- Non-continuous dependency on the initial-state
Numerical simulation of hybrid automata:
- simulations of ODEs
- zero-crossing detection
Simulators:
- Simulink
- Stateflow
- SHIFT
- Modelica
PART II – ANALYSIS & DESIGN
Properties of hybrid automata:
- sequence properties (safety, liveness)
- ensemble properties (stability)
Safety/Reachability:
- transition systems
- reachability algorithms)
- controller synthesis based on reachability
Lyapunov stability of ODEs:
- epsilon-delta and beta-function definitions
- Lyapunov’s stability theorem
- LaSalle’s invariance principle
- Stability of linear systems
- Lyapunov stability of ODEs
- Lyapunov stability of hybrid systems
Impact Maps:
- Fixed-point theorem
- Stability of periodic solutions
Switched systems:
- Linear Switched systems
- Lyapunov stability of switched systems
Stability under arbitrary switching:
- Instability caused by switching
- Common Lyapunov function
- Converse results
- Algebraic conditions
Controller realization for stable switching
Stability under slow switching:
- Dwell-time switching
- Average dwell-time
- Stability under brief instabilities
Stability under state-dependent switching:
- State dependent common Lyapunov function
- Multiple Lyapunov functions
- LaSalle’s invariance principle
Computational methods to construct multiple Lyapunov
functions—Linear Matrix Inequalities (LMIs)
PART III – APPLICATIONS
Vision-based control
Modeling of network traffic
Stochastic hybrid systems:
- Communication networks
- Networked control system
- Bio-chemical reactions
