ECE1648S - Nonlinear Control Systems

Last modified January 12, 2012.

Instructor
M. Maggiore GB437 maggiore (at) control.utoronto.ca

Lectures
Day and Time Room
Wed 10-13 WB144

Course Outline

The concepts and techniques presented in this course will be complemented by control design examples for synchronization, path following, and coordination.

  • Introduction to differentiable manifolds
  • The feedback equivalence problem
    • Feedback linearization
    • Stabilization and tracking for feedback linearizable systems
    • Application to robotics
  • Invariant and controlled invariant manifolds; the zero dynamics algorithm
    • Application to a synchronization problem
    • Application to virtual holonomic constraints for mechanical systems
  • Invariant distributions and quotient systems
  • Introduction to nonlinear controllability

Evaluation
There will be four homeworks (60%), a final project (30%), and a final presentation (10%). I will post a list of projects on the Blackboard website. The list will give you some ideas, and you can use it as a starting point to formulate a project proposal subject to my approval. You will produce a project report and will present your finding to the entire class at the end of the course. My evaluation of your project will be based on your document and your presentation.

References
  • Differential geometry
    • V.I. Arnold: Ordinary Differential Equations, MIT Press, 1978
    • J. M. Lee: Introduction to Smooth Manifolds, Springer, 2003
    • M. Spivak: A Comprehensive Introduction to Differential Geometry, vol. 1, Third Ed., Publish or Perish, 2005
    • V. Guillemin, A. Pollack: Differential Topology, Prentice Hall, 1974
    • W. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed., Academic Press, 1986
  • Geometric nonlinear control
    • Alberto Isidori: Nonlinear Control Systems, Third Edition, Springer Verlag, 1995
    • H. Nijmeijer, A.J. van der Schaft: Nonlinear Dynamical Systems, Springer Verlag, 1990
    • V. Jurdjevic: Geometric Control Theory, Cambridge University Press, 1996
    • A. Agrachev, Y. Sachkov: Control Theory from the Geometric Viewpoint, Springer, 2004
  • A comprehensive reference on nonlinear control systems
    • Hassan Khalil: Nonlinear Systems, Third Edition, Prentice Hall, 2002