NME130/Dynamical systems

Dynamical systems in two parallel tracks

• Continuous time, time-invariant systems (6 hours)
  • Differential equations and solutions
  • Stabilizability
  • Linearization
  • Controllability and Observability
  • Lyapunov equation/Lyapunov functions (show nonlinear case without proof)
• Finite state transition systems (6 hours)
  • Finite automata
  • Regular languages
  • Linear temporal logic specifications

Discussion

• Why linear systems?
  • May not be necessary
  • Existence and uniqueness are harder in the nonlinear case
  • Can probably start nonlinear, go linear by obs/ctr, then mention nonlinear again at the Lyapunov level
• Finite state machines
  • Talk about LTL, Bucchi automata, etc
• How much should we focus on the tools
  • Assume that people will do homework problems that make use of these
  • Don't need to spend time in lecture going through the details
  • No common tool set for many of these tools - could pose a problem
• Can we focus on similarities versus differences
  • Take a point view of rings and fields, instead of focusing on the differences

Possible links to hybrid systems (3 more hours?)

• After presenting both topics, link to case study and/or generalizations
  • Generalizations: numerical simulation, stability, etc
  • Case study: hybrid models for UAVs, biological systems