ON THE 'BANG-BANG' CONTROL PROBLEM

Let S be a physical system whose state at any time is described by an n-dimensional vector xt, where xt is determined by a linear differential equation Z Az, with A a constant matrix. Application of external influences will yield an inhomogeneous equation, Z Az f, where f, the forcing term, represents the control. A problem of some importance in the theory of control circuits is that of choosing f so as to reduce z to 0 in minimum time. If f is restricted to belong to the class of vectors whose ith components can assume only the values b sub i, the control is said to be of the bang-bang type. The case where all the solutions of Z Az approach zero as t approaches infinity is considered.