ME 601 Optimal Control

This course is designed to equip students with fundamental theories and computational methodologies that are used in (computer-aided) analysis and synthesis of optimal control systems. By the end of the course a solid understanding of the principles of optimal control in the context of variational calculus and experience with synthesis and implementation of optimal controllers are aimed. The course is appropriate for students in any engineering discipline with interests in robotics and controls.

After a short review of static optimization and numerical methods to address static optimization problems, students will be introduced to the principle of optimality and the Hamilton-Jacobi-Bellman equations in the context of dynamic programming. Calculus of variations will be studied in detail, emphasizing necessary conditions for an extrema and the Pontryagin’s minimum principle. Formulation of optimal control problems and performance measures will be covered. Sucient conditions for optimality will be covered. Special attention will be paid to linear regulator, minimum-time, and minimum control-e ort problems. Finally, optimal controllers will be synthesized using direct and indirect approaches and implemented as real-time controllers on a physical laboratory setup.

The emphasis of this course is not on the excessive mathematical abstraction, but rather, the aim is to capture the core elements of dynamic optimization and optimal control. An integrated understanding modeling, analysis, synthesis, and hardware-in-the-loop implementation of optimal control systems is sought. An intuitive understanding of the fundamental concepts, such as Pontryagin’s minimum principle, is aimed, since a solid understanding of such concepts help students better appreciate the reasoning behind system modeling and controller synthesis. Computer-aided (numerical) techniques and real-time hardware-in-the- loop implementation of the controllers are also emphasized such that students can address the control challenges of the real world, and experience implementation issues such as sensor noise and unmodeled system dynamics.