The bang–bang theorem via Baire category: a dual approach

Abstract

The paper develops a new approach to the classical bang–bang theorem in linear control theory, based on Baire category. Among all controls which steer the system from the origin to a given point $${\bar x}$$ , we consider those which minimize an auxiliary linear functional $${\phi}$$ . For all $${\phi}$$ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.