Applied Algebra Seminar: Algebraic Approaches to the Belgian Chocolate Problem

Seminar | May 4 | 5:15-6:15 p.m. | 891 Evans Hall

 Zachary Charles, University of Wisconsin

 Department of Mathematics

Control theory is concerned with systems that have built-in feedback that regulates their behavior. Control theorists study when the resulting feedback loop is stable. We will present the Belgian Chocolate Problem, a famous open problem concerning the stabilization of such systems. The problem asks for which values of a process parameter we can stabilize a specific feedback loop. In contrast to previous methods that use optimization to search over parameter spaces, we will discuss recent algebraic methods that have led to largest known parameter for which the system can be stabilized. We will present a theorem linking these algebraic “limiting cases” to stable feedback loops. We will also discuss connections between this method and optimization on semi-algebraic varieties.

This is joint work with Nigel Boston.