About this Course
4.8
22 ratings
4 reviews
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Flexible deadlines

Flexible deadlines

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Advanced Level

Advanced Level

Hours to complete

Approx. 22 hours to complete

Suggested: Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week....
Available languages

English

Subtitles: English...
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Advanced Level

Advanced Level

Hours to complete

Approx. 22 hours to complete

Suggested: Best completed in 4 weeks, with a commitment of between 2 and 5 hours of work per week....
Available languages

English

Subtitles: English...

Syllabus - What you will learn from this course

Week
1
Hours to complete
2 hours to complete

Nonlinear Stability Definitions

Discusses stability definitions of nonlinear dynamical systems, and compares to the classical linear stability definitions. The difference between local and global stability is covered. ...
Reading
12 videos (Total 67 min), 7 quizzes
Video12 videos
Module 1 Introduction1m
1: Overview of Nonlinear Control6m
1.1: Overview Stability Definition Discussion5m
1.2: Nonlinear Equations Representation8m
2: Definition: Neighborhood3m
3: Definitions: Lagrange Stability3m
4: Definitions: Lyapunov Stability5m
5: Definitions: Asymptotic Stability6m
6: Definitions: Global Stability2m
7: Linearizing a Dynamical System6m
Optional Review: Stability Definitions16m
Quiz7 practice exercises
Concept Check 1 - State Vector Representation10m
Concept Check 2 - State Neighborhood4m
Concept Check 3 - Lagrange Stability4m
Concept Check 4 - Lyapunov Stability6m
Concept Check 5 - Asymptotic Stability4m
Concept Check 6 - Global Stability Definitions10m
Concept Check 7 - Linearization6m
Week
2
Hours to complete
3 hours to complete

Overview of Lyapunov Stability Theory

Lyapunov's direct method is employed to prove these stability properties for a nonlinear system and prove stability and convergence. The possible function definiteness is introduced which forms the building block of Lyapunov's direct method. Convenient prototype Lyapunov candidate functions are presented for rate- and state-error measures....
Reading
14 videos (Total 129 min), 7 quizzes
Video14 videos
1: Overview of Definite Function15m
2: Lyapunov Function Definition10m
2.1: Lyapunov Asymptotic Stability17m
3: Lyapunov Stability of Linear System4m
4: Global Stability Applications2m
Optional Review: Definiteness7m
Optional Review: Stability Definitions3m
Optional Review: Lyapunov's Direct Method9m
5: General Elemental Velocity Lyapunov Function12m
5.1 Example: Multi-Link System3m
6: Rigid Body Detumble Control20m
7: State-Based Lyapunov Functions14m
Optional Review: Elemental Lyapunov Functions2m
Quiz7 practice exercises
Concept Check 1 - Definite Function16m
Concept Check 2 - Lyapunov Functions22m
Concept Check 3 - Asymptotic Stability14m
Concept Check 4 - Global Stability Applications14m
Concept Check 5 - General Elemental Rate2m
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8m
Concept Check 7 - General Elemental State Lyapunov Function4m
Week
3
Hours to complete
2 hours to complete

Attitude Control of States and Rates

A nonlinear 3-axis attitude pointing control law is developed and its stability is analyized using Lyapunov theory. Convergence is discussed considering both modeled and unmodeled torques. The control gain selection is presented using the convenient linearized closed loop dynamics....
Reading
8 videos (Total 82 min), 5 quizzes
Video8 videos
1: Nonlinear Rigid Body State and Rate Control14m
2: Global Stability of Nonlinear Attitude Control8m
2.1 Example: Nonlinear Regulation Control11m
2.2: Asymptotic Stability for Nonlinear Attitude Control5m
3: Unmodeled Disturbance Torque15m
4: Nonlinear Integral Control11m
5: Feedback Gain Selection13m
Quiz5 practice exercises
Concept Check 1 - General 3-Axis Attitude Control10m
Concept Check 2 - Asymptotic Stability14m
Concept Check 3 - Unknown External Torques8m
Concept Check 4 - Integral Feedback8m
Concept Check 5 - Feedback Gain Selection6m
Week
4
Hours to complete
4 hours to complete

Alternate Attitude Control Formulations

Alternate feedback control laws are formulated where actuator saturation is considered. Further, a control law is presented that perfectly linearizes the closed loop dynamics in terms of quaternions and MRPs. Finally, the 3-axis Lyapunov attitude control is developed for a spacecraft with a cluster of N reaction wheel control devices....
Reading
6 videos (Total 97 min), 4 quizzes
Video6 videos
1: Lyapunov Optimal Control30m
2: Example: Numerical Control Simulation8m
2.1: Linear Closed-Loop Dynamics21m
3: RW Feedback Control Law22m
Optional Review: Unconstrained Attitude Control13m
Quiz3 practice exercises
Concept Check 1 - Saturated Control16m
Concept Check 2 - Linearized Closed Loop Dynamics6m
Concept Check 3 - RW Feedback Control6m
4.8

Top Reviews

By SDFeb 4th 2018

Excellent teaching from Professor Schaub ! Course has been very well organised and touches on the important aspects of nonlinear control. Looking forward to more courses from you.\n\nThank you !

Instructor

Avatar

Hanspeter Schaub

Glenn L. Murphy Chair of Engineering, Professor
Department of Aerospace Engineering Sciences

About University of Colorado Boulder

CU-Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies....

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