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

Jan 22

HW 1 due

Stability Analysis

Jan 23

6 - Center Manifold Theory

Jan 28

7 - Mathematical Background

Jan 30

8 - Existence and Uniqueness Theorems for ODEs

Lyapunov Stability

Feb 4

9 - Lyapunov Stability Theory

Feb 6

10 - LaSalle-Krasovskii Invariance Principle

Feb 7

HW 2 due

Feb 11

11 - Lyapunov’s Linearization Method

Feb 13

12 - Time-Varying Systems Continued

Feb 18

13 - Time-Varying Systems and Lyapunov Design

Feb 20

14 - Backstepping

Feb 21

HW 3 due

Feb 25

Midterm Exam

Feedback Control

Feb 27

15 - Input-to-State Stability

Mar 4

16 - Feedback Linearization

Mar 6

17 - Feedback Linearization (continued)

Mar 11

18 - Full-State Feedback Linearization

Mar 13

19 - Full-State Feedback Linearization (continued)

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

Apr 10

25 - High-Order Control Barrier Functions

Hybrid Systems for Bipedal Locomotion

Apr 15

26 - Hybrid Systems and Zero Dynamics

Apr 17

27 - Control Lyapunov Functions for Hybrid Systems

Apr 18

HW 6 due

Apr 22

Final Exam Review

Apr 29

Final Exam