# Control of Nonlinear Spacecraft Attitude Motion

This course, offered by University of Colorado Boulder, delves into the programming of specific orientation and achieving precise aiming goals for spacecraft moving through three-dimensional space. By covering stability definitions of nonlinear dynamical systems and the application of Lyapunov's Direct Method, you'll gain a deep understanding of nonlinear 3-axis attitude pointing control law development. Additionally, you'll explore alternate feedback control laws and closed-loop dynamics.

Throughout the course, you'll differentiate between a range of nonlinear stability concepts and apply Lyapunov’s direct method to argue stability and convergence on a variety of dynamical systems. You'll also develop rate and attitude error measures for 3-axis attitude control using Lyapunov theory, and analyze rigid body control convergence with unmodeled torque.

• 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 3-axis attitude control using Lyapunov theory
• Analyze rigid body control convergence with unmodeled torque

Certificate Available ✔

##### Course Modules

This course is structured into four modules. Module 1 covers nonlinear stability definitions, Module 2 delves into Lyapunov Stability Theory, Module 3 explores attitude control of states and rates, and Module 4 focuses on alternate attitude control formulations.

#### Nonlinear Stability Definitions

This module introduces the course and provides an overview of nonlinear stability definitions. It covers the difference between local and global stability, analyzes and applies Lyapunov's Direct Method to prove stability properties, and develops a nonlinear 3-axis attitude pointing control law using Lyapunov theory. The module concludes with optional review sessions and concept checks to reinforce learning.

#### Overview of Lyapunov Stability Theory

This module delves into Lyapunov Stability Theory, providing an overview of definite functions, Lyapunov function definition, and applications of global stability. It explores Lyapunov stability of linear systems, as well as state-based Lyapunov functions and their applications. The module also includes optional reviews and concept checks for comprehensive understanding.

#### Attitude Control of States and Rates

This module focuses on attitude control of states and rates, covering topics such as nonlinear rigid body state and rate control, global stability of nonlinear attitude control, unmodeled disturbance torque, and feedback gain selection. It also includes concept checks for the application of learned concepts.

#### Alternate Attitude Control Formulations

In this module, you'll explore alternate attitude control formulations, including Lyapunov optimal control, numerical control simulation, linear closed-loop dynamics, and RW feedback control law. The module also includes an optional review and a final assignment to solidify the understanding of nonlinear control.

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