Functional analysis and the optimal control of linear discrete systems

Abstract

The optimal regulation of a linear discrete system in which one wishes to use either the minimum amount of fuel, energy or amplitude in the control has received much attention. It is readily shown that each of these control problems can be equated to that of finding a specific solution to a system of consistent linear equations in the control variables. Various algorithms have been developed which will yield an optimal control ; however, they tend to be computationally inefficient (for the minimum fuel and amplitude problems) and are therefore of little practical value. In this paper, a number of important properties related to the solution of a consistent system of linear equations will be developed. These properties are proven by appealing to same basic theorems from functional analysis and will be directly applicable to the above control problems. Algorithmic procedures for solving the minimum fuel (minimum l∞ solution) and minimum amplitude (minimum l;∞ solution) are then developed. These algorithmic ...