# Accession Number:

## AD0261851

# Title:

## A STUDY OF THE OPTIMAL CONTROL OF DYNAMIC SYSTEMS

# Descriptive Note:

# Corporate Author:

## HARVARD UNIV CAMBRIDGE MASS CRUFT LAB

# Personal Author(s):

# Report Date:

## 1961-02-10

# Pagination or Media Count:

## 1.0

# Abstract:

In this report, we study the problem of controlling the behavior of a general dynamic system subject to various physical constraints. The class of dynamic systems considered is assumed to obey the linear vector differential equation x equals Fx Du , x0 equals c where x is an n-vector called the state vector, F is a nxn matrix of constant elements, D is a nxr matrix of constant elements, u is a r-vector called the control vector. The constraints stipulated are, ut equals uiT for iT is less than or equal to t which is less than i 1T and the absolute value of ut is less than or equals to 1 for t greater than or equal to i.e., the control vector is constrained to be piecewise constant and amplitude limited. We are interested in the determination of ut subject to ii or iii of both such that the state vector xt attains the value zero in minimum time or the integral of some measure of the vector is a minimum over a period of time. A well-known example of this class of problems is the so-called bang-bang control problem. Author