Summary

This course provides a rigorous introduction to the analysis and control of nonlinear dynamical systems. Topics include the fundamental phenomena that distinguish nonlinear from linear systems, qualitative behavior of planar systems, Lyapunov stability theory, computational methods for stability and control, advanced nonlinear control design techniques, control Lyapunov and barrier functions, and analysis of uncertain systems.

Topics Covered

• Fundamental Properties of Nonlinear Systems:
  Nonlinear phenomena, planar systems, bifurcations, existence and uniqueness theorems. (Lectures 1-5)
  
  

• Lyapunov Stability Theory:
  Lyapunov’s direct and indirect methods, region of attraction, Lyapunov-based control design examples (backstepping and adaptive control), input-to-state stability. (Lectures 6-12)
  
  

• Sum-of-Squares Methods:
  Sum-of-squares techniques and semidefinite programming relaxations for Lyapunov analysis. (Lectures 13-14)
  
  

• Nonlinear Control Design:
  Feedback linearization, sliding mode control. (Lectures 15-17 and 19)
  
  

• Control Lyapunov and Barrier Functions:
  Advanced tools for nonlinear stabilization and safety. (Lectures 18 and 20-21)
  
  

• Dissipation Inequalities and Quadratic Constraints:
  Dissipation inequalities and quadratic constraints for analysis of uncertain systems. (Lectures 22-25)

References:  No textbook required, but the following may be useful:

1. H.K. Khalil, Nonlinear Systems, Prentice Hall, 3rd edition, 2002

2. Sastry, Nonlinear Systems: Analysis, Stability and Control, Springer, 1999