NME130/Dynamical systems

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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


  • 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