Calendar

Introduction to Nonlinear Systems

Jan 7: 1 - Intro to Nonlinear Systems
Jan 9: 2 - Nonlinear Phenomena

Second-Order Systems

Jan 14: 3 - Periodic Orbits in the Plane
Jan 16: 4 - Periodic Orbits in the Plane Continued
Jan 21: 5 - Bifurcations

Stability Analysis

Jan 23: 6 - Center Manifold Theory
Jan 24: HW 1 due

Fundamental Properties

Jan 28: 7 - Mathematical Background; 7b - Existence and Uniqueness Theorems for ODEs

Lyapunov Stability

Jan 30: 8 - Lyapunov Stability Theory
Feb 4: 9 - LaSalle-Krasovskii Invariance Principle
Feb 6: 10 - Lyapunov’s Linearization
Feb 7: HW 2 due
Feb 11: 11 - Time-Varying Systems
Feb 13: 12 - Time-Varying Systems and Lyapunov Design
Feb 18: 13 - Backstepping
Feb 20: 14 - Midterm Review
Feb 21: HW 3 due
Feb 25: Midterm Exam

Feedback Control

Feb 27: 15 - Introduction to Feedback Linearization
Mar 4: 16 - Feedback Linearization 1
Mar 6: 17 - Feedback Linearization 2
Mar 11: 18 - Full-State Feedback Linearization 1
Mar 13: 19 - Full-State Feedback Linearization 2
Mar 14: HW 4 due

Optimization-Based Control

Mar 25: 20 - Control Lyapunov Functions
Mar 27: 21 - A Primer on Convex Optimization
Apr 1: 22 - Classes of Convex Optimization Problems

Safety-Critical Control

Apr 3: 23 - Barrier Functions
Apr 4: HW 5 due
Apr 8: 24 - Control Barrier Functions

Hybrid Systems for Bipedal Locomotion

Apr 10: 25 - Hybrid Systems and Zero Dynamics
Apr 15: 26 - Control Lyapunov Functions for Hybrid Systems
Apr 17: 27 - Final Exam Review
Apr 18: HW 6 due
Apr 22: Interactive Practice Problems (Kahoot)
Apr 29: Final Exam