# Accession Number:

## AD0604388

# Title:

## ON THE 'BANG-BANG' CONTROL PROBLEM

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CA

# Personal Author(s):

# Report Date:

## 1955-03-02

# Pagination or Media Count:

## 19.0

# Abstract:

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.

# Descriptors:

# Subject Categories:

- Human Factors Engineering and Man Machine Systems