**Course Title:** MAE 6570 Optimal Spacecraft Guidance

**Course Setting:** Tuesdays and Thursdays 1:30 to 2:45 PM in ENGR 106

Office hours are Tuesdays 2:45 to 4:00 PM and Thursdays 2:45 to 3:25 PM in ENGR 419H. You may also call, email, or schedule an appointment.

**Targeted Audience:** The course is targeted at graduate students with an aerospace engineering emphasis. The course is appropriate for students preparing for industry and research work in the guidance, navigation, and control areas. In other words, this is a specialist course not a generalist course. Although prerequisites are minimal, we will need information from optimization theory, space dynamics, control, and optimal control. The requisite information will be shared in notes and lecture, but the course is fast-paced and the successful student will search on their own to fill in gaps.

**Course Outcomes:** Students should be comfortable with optimization and optimal control as they apply to spacecraft guidance problems. As such, they should be able to identify problems, model them, and solve them analytically or numerically. Students should be familiar with modern advances in the guidance field, have the ability to read the literature, and contribute to the literature with faculty mentorship.

**Course Description:** Students will learn the mathematical theory of optimization, optimal control, and computational techniques for solving optimal spacecraft guidance problems. The theoretical topics include mathematical foundations, the Karush-Kuhn-Tucker and Fritz John conditions for constrained optimization problems, and the Pontryagin Minimum Principle. The computational techniques discussed include those of linear, convex, and nonlinear programming, indirect shooting, and direct transcription. The emphasis of the course is to develop strong fundamentals, modeling abilities, and solution strategies for spacecraft guidance problems.

**Prerequisites:** The incoming student needs a *solid* foundation in multivariable calculus, linear algebra, differential equations, and numerical methods. The Utah State University requirements are

MATH 2210 Multivariable Calculus

MATH 2250 Linear Algebra and Differential Equations

**Textbooks:** You are not required to purchase a textbook. There are many good books in optimization and optimal control – some of which are free online or at low cost as paper backs.

Convexity and Optimization in Rn by Berkovitz

Optimal Control Theory by Berkovitz

Calculus of Variations and Optimal Control Theory by Liberzon

Optimal Control by Athans and Falb

Foundations of Optimal Control Theory by Lee and Markus

The Mathematical Theory of Optimal Processes by Pontryagin

The book by Pontryagin and his colleagues was the seminal work in optimal control. It is mathematically advanced but readable and still relevant. The book by Liberzon is available for free online and is the most modern and accessible introduction to optimal control. The books by Athans, Falb, Lee, and Markus were two of the earliest books on optimal control in the United States. They contain numerous important results for modern researchers. Lastly, the two books by Berkovitz provide numerous other results still used by modern researchers.

**Student Evaluations:** Student performance is evaluated in homework assignments, a project, and an exam. The purpose of the homework is to practice and learn by doing. The homework can be worked individually or in a group, but the submission must represent the individual understanding. Homework topics include mathematics, problem solving, and programming (in MATLAB or Python). There are five homework assignments each worth 10% of the final grade.

There is one project report that must be of “conference” quality and typeset using LaTeX. The project report can be on a topic of choice or a reworking of existing published papers. The purpose of the project is to familiarize students with technical writing in LaTeX and introduce them to the spacecraft guidance literature. The project is worth 25% of the final grade.

There is one final exam. The exam is a comprehensive oral exam that will be conducted in the week prior to the official final exam week. The exam will include conversation with the instructor and problem-solving on the white board.

Homework. 50%

Project. 25%

Exam. 25%

Grading is done so that the grades reflect the individual’s understanding of the course concepts. Grading is *not* done to reflect performance relative to peers in the class.

There are many things in life more important than a grade in Optimal Spacecraft Guidance class, and achieving a good grade is not worth sacrificing one’s integrity. The instructor and students are expected to adhere to the Honor Pledge: “I pledge, on my honor, to conduct myself with the foremost level of academic integrity.”

**Course Schedule:** The following schedule is a rough outline for the course. It is subject to change throughout the semester.

Weeks 1-3: Optimization

Weeks 4-6: Optimal Control of Discrete Systems

Weeks 7-12: Optimal Control of Continuous Systems

Weeks 13-15: Applications from the literature

Week 16: No class