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University of Colorado Boulder - Control of Nonlinear Spacecraft Attitude Motion 

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Control of Nonlinear Spacecraft Attitude Motion


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Control of Nonlinear Spacecraft Attitude Motion

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Control of Nonlinear Spacecraft Attitude Motion
Course details

Skills you will learn
More about this course
  • This course trains you in the skills needed to program specific orientation and achieve precise aiming goals for spacecraft moving through three dimensional space. First, we cover stability definitions of nonlinear dynamical systems, covering the difference between local and global stability. We then analyze and apply Lyapunov's Direct Method to prove these stability properties, and develop a nonlinear 3-axis attitude pointing control law using Lyapunov theory. Finally, we look at alternate feedback control laws and closed loop dynamics.
  • After this course, you will be able to...
  • * Differentiate between a range of nonlinear stability concepts
  • * Apply Lyapunov?s direct method to argue stability and convergence on a range of dynamical systems
  • * Develop rate and attitude error measures for a 3-axis attitude control using Lyapunov theory
  • * Analyze rigid body control convergence with unmodeled torque
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Control of Nonlinear Spacecraft Attitude Motion

Nonlinear Stability Definitions

Course Introduction

Module 1 Introduction

1: Overview of Nonlinear Control

1.1: Overview Stability Definition Discussion

1.2: Nonlinear Equations Representation

2: Definition: Neighborhood

3: Definitions: Lagrange Stability

4: Definitions: Lyapunov Stability

5: Definitions: Asymptotic Stability

6: Definitions: Global Stability

7: Linearizing a Dynamical System

Optional Review: Stability Definitions

Concept Check 1 - State Vector Representation

Concept Check 2 - State Neighborhood

Concept Check 3 - Lagrange Stability

Concept Check 4 - Lyapunov Stability

Concept Check 5 - Asymptotic Stability

Concept Check 6 - Global Stability Definitions

Concept Check 7 - Linearization

Overview of Lyapunov Stability Theory

Module 2 Introduction

1: Overview of Definite Function

2: Lyapunov Function Definition

2.1: Lyapunov Asymptotic Stability

3: Lyapunov Stability of Linear System

4: Global Stability Applications

Optional Review: Definiteness

Optional Review: Stability Definitions

Optional Review: Lyapunov's Direct Method

5: General Elemental Velocity Lyapunov Function

5.1 Example: Multi-Link System

6: Rigid Body Detumble Control

7: State-Based Lyapunov Functions

Optional Review: Elemental Lyapunov Functions

Concept Check 1 - Definite Function

Concept Check 2 - Lyapunov Functions

Concept Check 3 - Asymptotic Stability

Concept Check 4 - Global Stability Applications

Concept Check 5 - General Elemental Rate

Concept Check 6 - Rigid Body Elemental Rate Lyapunov Function

Concept Check 7 - General Elemental State Lyapunov Function

Attitude Control of States and Rates

Module 3 Introduction

1: Nonlinear Rigid Body State and Rate Control

2: Global Stability of Nonlinear Attitude Control

2.1 Example: Nonlinear Regulation Control

2.2: Asymptotic Stability for Nonlinear Attitude Control

3: Unmodeled Disturbance Torque

4: Nonlinear Integral Control

5: Feedback Gain Selection

Concept Check 1 - General 3-Axis Attitude Control

Concept Check 2 - Asymptotic Stability

Concept Check 3 - Unknown External Torques

Concept Check 4 - Integral Feedback

Concept Check 5 - Feedback Gain Selection

Alternate Attitude Control Formulations

Module 4 Introduction

1: Lyapunov Optimal Control

2: Example: Numerical Control Simulation

2.1: Linear Closed-Loop Dynamics

3: RW Feedback Control Law

Optional Review: Unconstrained Attitude Control

Concept Check 1 - Saturated Control

Concept Check 2 - Linearized Closed Loop Dynamics

Concept Check 3 - RW Feedback Control

Control of Nonlinear Spacecraft Attitude Motion
Admission Process

    Important Dates

    May 25, 2024
    Course Commencement Date

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