Personal Notes

Linear Control Theory

Preliminary

• Why Linear Control Theory?
• Solution for the Linear Dynamical Systems

Linear Time-invariant (LTI) Systems

• Analysis of LTI Systems
  • Dynamics of LTI Systems
  • Eigenvalue and Eigenvector Analysis
  • Stability of LTI Systems
  • Transfer Function and State-space representation
  • Bode Plot
    
• Controllability and Observability of LTI Systems
  • Controllability
  • Observability
  • Luenberger observer

Nonlinear Control Theory

Preliminary

• Why Nonlinear Control?

Existence and Uniqueness Theorems

• Preliminary Math
• Contraction Mapping Theorem
• Local and Global Existence and Uniqueness of Solutions

Optimal Control Theory

• Hamilton-Jacobi-Bellman Equation

Dynamics (Classical Mechanics)

Dynamics of a Single Particle

• Newton’s Laws of Motion, Linear Momentum Principle
• Conservative Force
• Angular Momentum Principle
• Newton’s Laws of Motion in a Non-inertial Frame

Kinematics of a Rigid Body — Rotation

• Definition of Rigid Body
• Rotation Matrix and SO(3) Groups
• Exponential Coordinates for Rotation
• Superposition Principle of Angular Velocity

Kinematics of a Rigid Body — Translation and Rotation

• Rigid Body Transformation
• Rigid Body Kinematics in 3D Space

Dynamics of a Rigid Body

• Euler’s Laws of Motion, Center of Mass
• Moment of Inertia of a Rigid Object
• Angular Momentum Principle of Rigid Object
• Euler’s Equations for Rigid Body Dynamics

Analytical Mechanics

• Generalized Coordinates and Configuration Space
• Principle of Virtual Work
• Variational Principle and Euler-Lagrange Equation
• D’Alembert’s Principle
• Gauss’ Principle of Least Constraint
• Gibbs-Appell Equations of Motion
• Lagrangian Mechanics
• Hamiltonian Mechanics

Example Problems

• Cart and Pendulum
• Rolling Cylinder

Robotics

Forward Kinematics

• Forward Kinematics and Jacobian
• Denavit-Hartenberg Parameters

Managing Kinematic Redundancy

• Kinematic Redundancy and Null-space Projection

Equations of Motion of the Robotic Manipulator

• Deriving the Robotic Manipualtor Equation
• Some Properties of the Robotic Manipulator Equation

Impedance Control

• Theory
• Joint-space Impedance Control
• Task-space Impedance Control — Position, without Kinematic Redundancy
• Task-space Impedance Control — Orientation, SO(3)

Controllers

• Sliding Variable and Sliding-mode Control
• Adaptive Control
• Operational Space Control

Dynamic Movement Primitives

• Theory
• Applications

Inertial Parameter Estimation

• Physical feasibility of robot base inertial parameter

Miscellaneous Maths

Differential Equations

• First-order Linear Differential Equations

Linear Algebra

• Before Going through the Notes
• Fields and Vector Spaces
• Span, Linear Independence and Basis
  
• Covariance and Contravariance of vectors

Others

• Complex Number
• Laplace Transform
• Lagrange Multiplier – Equality Constraints
• Inequality Constraints and Karush-Kuhn-Tucker Conditions

Machine Learning - Personal Notes

• Preliminary - Markov Processes
• Q-learning