Prerequisites: IT Upper Division or graduate student, AEM 4321

Parameter optimization problems. Topics in calculus of variations; necessary conditions of nonlinear optimal control problems; classification of trajectory optimization algorithms; steady-state aircraft flight; minimum-time climb aircraft trajectory; aero-assisted orbital transfer trajectories; optimal space trajectories.

Textbook: Required: Dynamic Optimization, Bryson, Addison-Wesley, ISBN: 9780201597905

Summary

Optimal control theory is a classical subject of mathematical studies and was partially responsible for the advances of science in the early phases. Nowadays, applied optimal control methods are essential parts of the standard tool set of analysis and synthesis in almost every discipline of science and engineering. In aerospace engineering, optimal control methods can be used to develop guidance strategies.

This course introduces the ideas and important results of nonlinear optimal control requiring only a background in ordinary calculus. In addition, it uses simple examples that make the learning of optimal control theory comfortable.

Topics of this course are divided into three parts. Part I reviews the fundamentals of parameter optimization. Part II gradually and systematically introduces the fundamental theories of continuous-time nonlinear optimal control from the simplest version to the general version. Numerous examples derived from physical systems help students learn optimal control theories step by step. Finally, Part III discusses schemes of approximate solution methods of optimal control problems.

Throughout the course, applications of optimal control theories in optimizing vehicle motion trajectories, especially in developing optimal flight strategies for unmanned aerial vehicles (UAVs), will be discussed.

This course is open to senior undergraduate students and all levels of graduate students. Those who are interested in this course should have a strong background in ordinary calculus and a familiarity with ordinary differential equations and linear algebra. Knowledge from a first course in automatic control is desirable but not required.

Grading of the course is based on demonstrated proficiency in solving optimization problems on a blackboard, two midterm exams, and a final exam or project.