Difference between revisions of "NME130/Dynamical systems"

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** Don't need to spend time in lecture going through the details
 
** 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
 
** 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?)
 
Possible links to hybrid systems (3 more hours?)

Latest revision as of 22:37, 16 June 2009

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