Time and place: Friday, May 14, 10:50-11:50, 202 Chernoff Hall
Title: Reach Control Problem (1 hour)
Abstract: The field of control theory has focused historically on problems of tracking and regulation. An example of regulation would be setting a desired speed in a vehicle cruise control system. Optimizing a solar cell performance by rotating its surface to continually face the sun during daylight hours is an example of tracking. Tracking and regulation are very simple control system specifications. As control systems become more integrated within high-end engineering systems as well as consumer products, they are expected to achieve richer specifications that consider safety requirements, startup procedures, and so forth. Good examples of complex specifications would be the startup of a chemical or nuclear reaction, requirements for an automatic parking system, or transition between different gaits in a bipedal robot.
At the core of the research thrust to enrich control specifications is the
Reach Control Problem. This problem is formulated on polyhedra or simplices
in the state space and is focused on the class of affine systems. Roughly
speaking, the problem is for an affine system
In this talk, I will give an overview of results on the reach control problem. I will begin with basic principles and then move on to discussing what is known about solvability by affine feedbacks, continuous state feedbacks, and open-loop controls.