# Accession Number:

## AD0258557

# Title:

## FINAL VALUE CONTROL PROBLEMS AND THE METHOD OF CONSTRAINED DESCENT

# Descriptive Note:

# Corporate Author:

## HARVARD UNIV CAMBRIDGE MASS CRUFT LAB

# Personal Author(s):

# Report Date:

## 1961-04-10

# Pagination or Media Count:

## 1.0

# Abstract:

Solution of the vector matrix equation Ax equals b is discussed, subject to the constraint that x is greater than or equal to L- and less than or equal to L, where O is greater than or equal to L- and less than or equal to L, and L-L- is greater than O. Here, A is an r x n matrix b is an r vector L, L-, and x are n vectors. Such problems often arise in the consideration of final value control systems. In such case b is visualized as the vector representing the desired final state of the system x, the control to be applied at successive control intervals l,..,n A, the matrix of influence coefficients which represent the effect of the components of x on the final state of the system L and L-, the limits for the control vector x, reflecting practical constraints for allowable variations of x. Solutions to the above mentioned problem may be nonexistent or infinite in number. The purpose of this paper is to illustrate a systematic way of solving such a problem which does not require advanced knowledge concerning the existence of solutions. Author