Course Information

Description

This course will introduce the students to the fundamental concepts and methods in modern control and estimation theory. Topics include state-space modeling of dynamical systems, least-square estimation and system identification, state-feedback and output-feedback controller design, observer design, linear quadratic regulators, and Kalman filter. The course will also connect these control and estimation methods to applications in robotics, mechanical, electrical, and aerospace systems.

Lecture Notes

• Lecture 0: Course Information [PDF]
• Lecture 1: Linear Algebra Review [PDF] [P3-update] [P1P2-notes] [P3-notes]

Linear independence, Vector space, Solution space of Ax = b, Inner product, Simple geometric sets, Quadratic sets


• Lecture 2: State Space Models [PDF] [Notes]

State space models, From continuous to discrete time model, From nonlinear to linear model, Transfer function


• Lecture 3: Least Squares and Basic System Identification [PDF] [Notes]

Least squares problem formulation, Solution to linear least square problems, Applications to System ID, Nonlinear least squares


• Lecture 4: Stability, Controllability, and Observability [PDF] [Notes]

State space solutions, Internal stability, Controllability, Observability, Invariance under similarity transformation


• Lecture 5: State-Feedback and Output-Feedback Control [PDF] [Notes]

Full State-feedback: Eigenvalue Assignment, Luenberger Observer Design, Output-feedback Control and Separation Principle


• Lecture 6: Control Design and Testing in Drake with Python [PDF] [Notes]

Short Introduction to Drake, Observer and Controller Design, From Regulation to Tracking Control, Examples


• Lecture 7.1: Probability Review [PDF] [Notes]

Probability and Conditional Probability, Random Variables and Random Vectors, Conditional Expectation, Covariance Matrix


• Lecture 7.2: Kalman Filter [PDF] [Notes]

Minimum Mean Squared Estimation (MMSE), Gaussian Random Vectors, Kalman Filter Derivation, Kalman Filter Implementation


• Lecture 7.3: Extended Kalman Filter [PDF] [Notes]

Extended Kalman Filter Derivation, Application Examples, Implementation


• Lecture 8: Linear Quadratic Regulator [PDF] [Notes]

General Discrete-Time Optimal Control Problem, Dynamic Programming, Linear Quadratic Regulator Derivation and Implementation

Tutorials

• Tutorial 1: Python, Numpy and Matplotlib [file]
• Tutorial 2: Read Files and Animation [file]
• Tutorial 3: Solving Nonlinear Least Square Problems [file]
• Tutorial 4: Install Drake on Your Computer [PDF]

References:

• "Linear Algebra", Gilbert Strang, Massachusetts Institute Technology.
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
•  Lecture notes, and papers distributed in class.