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 x¯ , we consider those which minimize an auxiliary linear functional ϕ. For all ϕ in a residual set, we show that the minimizing control is unique and takes values within a set of extreme points.
All Science Journal Classification (ASJC) codes
- Applied Mathematics