Nonlinear Control (MAE 544 | Princeton University | Fall 2017)

Core Topics
      ▸ Brief overview of relevant topics from linear algebra and advanced calculus
      ▸ Introduction to differential geometry - smooth manifolds and tangent/cotangent spaces, vector fields
      ▸ Lie groups and related concepts
      ▸ Lie bracket of vector fields
      ▸ Controllability properties of nonlinear systems
      ▸ Lyapunov stability theory and local stabilization
      ▸ Passivity and stabilization of dissipative systems
      ▸ Energy shaping and controlled Lagrangian
      ▸ Feedback linearization

Lecture Notes and Reading Material
      ▸ Lecture 1-2: Background and A Brief Review of Linear Algebra and Calculus
              ▪ September 14: Lecture Note - 1 (Basic Introduction; Examples of Nonlinear Systems)
                      Reading Material: Paper-1, Paper-2, Paper-3
              ▪ September 19: Lecture Note - 2 (Group, Ring, Field; Vector Space; Normed and Inner-Product Space)
      ▸ Lecture 3-8: Introduction to Differential Geometry
              ▪ September 21: Lecture Note - 3 (Dynamics on Non-Euclidean Space - Rigid Body Dynamics)
              ▪ September 26: Lecture Note - 4 (Manifolds; Charts and Atlases)
              ▪ September 28: Lecture Note - 5 (Charts and Atlases Contd.; Smooth Structures; Smooth Functions)
              ▪ October 05: Lecture Note - 6 (Tangent Vectors - Tangents to Smooth Curves, Derivation)
              ▪ October 10: Lecture Note - 7 (Tangent Space; Derivative of Smooth Functions; Tangent Bundle)
              ▪ October 12: Lecture Note - 8 (Vector Field; Cotangent Space; Cotangent Bundle; Differential 1-Form)
      ▸ Lecture 9-11: Control Systems as Vector Fields
              ▪ October 17: Lecture Note - 9 (Vector Fields as Derivations; Affine Control Systems; Intro. to Lie-Bracket)
                      Reading Material: Paper-4, Paper-5, Paper-6, Paper-7, Paper-8, Paper-9, Paper-10
              ▪ October 19: Lecture Note - 10 (Lie-Bracket of Vector Fields; Lie-Algebra)
                      Reading Material: Paper-11, Paper-12, Paper-13, Paper-14
              ▪ October 24: Lecture Note - 11 (Lie-Group; Left-Invariant Vector Fields; Integral Curves)
                      Reading Material: Paper-15, Paper-16, Paper-17
      ▸ Lecture 12-14: Nonlinear Controllability
              ▪ October 25: Lecture Note - 12 (Exponential Map; Distribution; Frobenius Theorem; Intro. to Controllability)
                      Reading Assignment: Chapter 8 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
              ▪ October 26: Lecture Note - 13 (Accessibility, Controllability and STLC; Lie-Algebraic Rank Condn.)
              ▪ November 07: Lecture Note - 14 (Stronger Form of Accessibility; More results on Controllability; Examples)
                      Reading Assignment: Chapter 3.1 of "Nonlinear Dynamical Control Systems" (Ref.#1)
                      Reading Assignment: Notes on Nonlinear Controllability: Andrew D. Lewis
      ▸ Lecture 15-16: Stabilization using Lyapunov Stability Theory
              ▪ November 09: Lecture Note - 15 (Stability in the Sense of Lyapunov; Lyapunov’s Direct Method)
                      Reading Assignment: Chapter 5.1-5.3 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
                      Reading Material: Paper-18, Paper-19, Paper-20, Paper-21
              ▪ November 14: Lecture Note - 16 (Lyapunov’s Indirect Method; Feedback Stabilization; Domain of Attraction)
                      Reading Assignment: Chapter 5.7-5.9 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
                      Reading Assignment: Chapter 6.1 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
      ▸ Lecture 17-18: Passivity and Dissipative System
              ▪ November 16: Lecture Note - 17 (L-p Spaces; Input-output Stability; Small Gain Theorem)
                      Reading Assignment: Chapter 4.2-4.3 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
              ▪ November 21: Lecture Note - 18 (Passivity and Dissipation Inequality; Input-to-State Stability (ISS))
                      Reading Assignment: Chapter 4.4 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
      ▸ Lecture 19-21: Control Lyapunov and Energy Shaping Methods
              ▪ November 28: Lecture Note - 19 (Control Lyapunov Function (CLF); Backstepping)
                      Reading Assignment: Chapter 6.8 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)
                      Reading Material: Paper-22, Paper-23, Paper-24
              ▪ November 29: Lecture Note - 20 (Passivity Based Control; Intro. to Controlled Lagrangian)
              ▪ November 30: Lecture Note - 21 (Controlled Lagrangian; Intro. to Feedback Linearization)
      ▸ Lecture 22-24: State and Output Feedback Linearization
              ▪ December 5: Lecture Note - 22 (Feedback Linearization for SISO Systems; Normal Form)
              ▪ December 6: Lecture Note - 23 (State-Space Exact Linearization; Zero Dynamics)
              ▪ December 7: Lecture Note - 24 (Zero Dynamics; Tracking and Stabilization)
                      Reading Assignment: Chapter 9 of "Nonlinear Systems: Analysis, Stability, and Control" (Ref.#3)

Homework Problem Sets
      ▸ Homework 1: Problem Set # 1 (Due: 10/05/2017)
      ▸ Homework 2: Problem Set # 2 (Due: 10/24/2017)
      ▸ Homework 3: Problem Set # 3 (Due: 11/09/2017)
      ▸ Homework 4: Problem Set # 4 (Due: 12/07/2017)
      ▸ Homework 5: Problem Set # 5 (Due: 12/14/2017)

References
      ▸ (1) Nijmeijer, H., van der Schaft, A. (1990) Nonlinear Dynamical Control Systems, Springer New York.
      ▸ (2) Isidori, A. (1995) Nonlinear Control Systems, Springer-Verlag London.
      ▸ (3) Sastry, S. S. (1999) Nonlinear Systems: Analysis, Stability, and Control, Springer-Verlag New York.
      ▸ (4) Schutz, B. F.(1980) Geometrical Methods of Mathematical Physics, Cambridge University Press.
      ▸ (5) Guillemin, V., Pollack, A. (Reprint, 2010) Differential Topology, American Mathematical Society.