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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 26 hours to complete

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

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 26 hours to complete

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

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
2 hours to complete

## Nonlinear Stability Definitions

12 videos (Total 67 min), 7 quizzes
12 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
7 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 - Linearization20m
Week
2
5 hours to complete

## Overview of Lyapunov Stability Theory

14 videos (Total 129 min), 7 quizzes
14 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
6: Rigid Body Detumble Control20m
7: State-Based Lyapunov Functions14m
Optional Review: Elemental Lyapunov Functions2m
7 practice exercises
Concept Check 1 - Definite Function20m
Concept Check 2 - Lyapunov Functions45m
Concept Check 3 - Asymptotic Stability40m
Concept Check 4 - Global Stability Applications30m
Concept Check 5 - General Elemental Rate5m
Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function8m
Concept Check 7 - General Elemental State Lyapunov Function20m
Week
3
11 hours to complete

## Attitude Control of States and Rates

8 videos (Total 82 min), 5 quizzes
8 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
5 practice exercises
Concept Check 1 - General 3-Axis Attitude Control1h 30m
Concept Check 2 - Asymptotic Stability1h 30m
Concept Check 3 - Unknown External Torques2h 8m
Concept Check 4 - Integral Feedback2h 30m
Concept Check 5 - Feedback Gain Selection2h 30m
Week
4
10 hours to complete

## Alternate Attitude Control Formulations

6 videos (Total 97 min), 4 quizzes
6 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
3 practice exercises
Concept Check 1 - Saturated Control3h 45m
Concept Check 2 - Linearized Closed Loop Dynamics2h 30m
Concept Check 3 - RW Feedback Control20m
4.7
8 Reviews

### Top reviews from Control of Nonlinear Spacecraft Attitude Motion

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

### Hanspeter Schaub

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

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....

## About the Spacecraft Dynamics and Control Specialization

Spacecraft Dynamics and Control covers three core topic areas: the description of the motion and rates of motion of rigid bodies (Kinematics), developing the equations of motion that prediction the movement of rigid bodies taking into account mass, torque, and inertia (Kinetics), and finally non-linear controls to program specific orientations and achieve precise aiming goals in three-dimensional space (Control). The specialization invites learners to develop competency in these three areas through targeted content delivery, continuous concept reinforcement, and project applications. The goal of the specialization is to introduce the theories related to spacecraft dynamics and control. This includes the three-dimensional description of orientation, creating the dynamical rotation models, as well as the feedback control development to achieve desired attitude trajectories....