24-677 Modern Control for Robotics, Fall 2021

Course Overview

Course banner for 24-677 Modern Control Theory

Instructor: Prof. Ding Zhao

Teaching Assistant: Peide Huang

Description: This course offers a practical introduction to the analysis and design of model-based control for linear systems. Topics include modeling and linearization of multi-input multi-output dynamic systems using the state-variable description, fundamentals of linear algebra, analytical and numerical solutions of systems of linear time-invariant differential and difference equations, structural properties of linear dynamic physical systems (controllability, observability and stability), canonical realizations, and design of state feedforward/feedback, optimal, and stochastic controllers and observers, including pole placement, LQR, MPC, Kalman filter, adaptive control approaches. Students will learn how to design linear controllers and implement them to solve real-world problems in control and robotics.

Objectives: The objectives of this course are to develop students' knowledge of multi-input / multi-output linear systems and their control, to enhance students' knowledge of engineering applications of linear algebra, and to prepare students for further graduate study in control systems, robotics, machine learning, and signal processing.

Outcomes: Upon completion of this course, the student should be able to:

Compare state space and transfer function approaches to the study of linear control systems and their relative advantages
Assess the stability of systems using various stability definitions
Determine the controllability and observability of a linear system
Design feedback controllers and observers for linear systems
Design optimal controller and stochastic observer for linear systems
Design model-based adaptive controlled for linear systems
Design controllers to solve real-world problems and implement them in Python and Webot

Textbook: No textbook. Lecture slides will be available on Canvas.

Lecture schedule for Fall 2021

Lecture 1 - Tuesday, Sep 1, 2020: Overview, types of system, state space representation [Slides]

Lecture 2 - Thursday, Sep 3, 2020: State space representation, examples, linearization, solution of CT LTI, exponential of matrix [Slides]

Lecture 3 - Tuesday, Sep 8, 2020: Eigen-values/vectors, determinant, linear independence [Slides]

Lecture 4 - Thursday, Sep 10, 2020: CH theorem [Slides]

Lecture 5 - Tuesday, Sep 15, 2020: Similarity transformation, matrix inverse, diagonalizability [Slides]

Lecture 6 - Thursday, Sep 17, 2020: Jordan decomposition, DT-LTI [Slides]

Lecture 7 - Tuesday, Sep 22, 2020: Controllability/observability definition, matrix test, solution of linear equations, SVD [Slides]

Lecture 8 - Thursday, Sep 24, 2020: PBH test, Jordan form test [Slides]

Lecture 9 - Tuesday, Sep 29, 2020: Laplace transformation, transfer function, ss2tf, controllable canonical forms [Slides]

Lecture 10 - Thursday, Oct 1, 2020: Observable canonical form, MIMO, Kalman decomposition, minimal realization [Slides]

Lecture 11 - Tuesday, Oct 6, 2020: Lyapunov stable, stability of Linear Time-Invariant systems [Slides]

Lecture 12 - Thursday, Oct 8, 2020: LTV example, stabilizability/detectability, Lyapunov’s Indirect/direct method [Slides]

Lecture 13 - Tuesday, Oct 13, 2020: Instability, BIBO, BIBS [Slides]

Lecture 14 - Thursday, Oct 15, 2020: Description of the project, PID control, pole placement [Slides]

Lecture 15 - Tuesday, Oct 20, 2020: Luenberger observer, separation principle [Slides]

Lecture 16 - Thursday, Oct 22, 2020: Mid-term exam

Lecture 17 - Tuesday, Oct 27, 2020: Reduced order observer, MIMO pole placement [Slides]

Lecture 18 - Thursday, Oct 29, 2020: Finite-horizon discrete-time linear quadratic regulator [Slides]

Lecture 19 - Tuesday, Nov 3, 2020: MPC, tracking [Slides]

Lecture 20 - Thursday, Nov 5, 2020: IH DT LQR [Slides]

Lecture 21 - Tuesday, Nov 10, 2020: FH/IH CT LQR [Slides]

Lecture 22 - Thursday, Nov 12, 2020: Kalman Filter [Slides]

Lecture 23 - Tuesday, Nov 17, 2020: Extended KF, UKF, SLAM [Slides]

Lecture 24 - Thursday, Nov 19, 2020: Adaptive control [Slides]

Lecture 25 - Tuesday, Nov 24, 2020: Adaptive control [Slides]

Thursday, Nov 26, 2020: Thanksgiving Holiday; No Classes

Lecture 26 - Tuesday, Dec 1, 2020: Alumni events

Lecture 27 - Thursday, Dec 3, 2020: Guest Speaker

Lecture 28 - Tuesday, Dec 8, 2020: Application of model-based methods in AIML - an introduction [Slides]

Lecture 29 - Thursday, Dec 10, 2020: Review of the whole course, outraduction [Slides]