Numerical Properties of the Ritz-Trefftz Algorithm for Optimal Control

In this paper the Ritz-Trefftz algorithm is applied
to the computer solution of the state regulator 
problem.  The algorithm represents a modification of
the Ritz direct method and is designed to improve 
the speed of solution and the storage requirements to
the point where real-time implementation becomes 
feasible.  The modification is shown to be more stable
computationally than the traditional Ritz approach. 
 The first concern of the paper is to describe the
algorithm and establish its properties as a valid 
and useful numerical technique.  In particular such useful
properties as definiteness and reasonableness 
of condition are established for the method.  The second
part of the paper is devoted to a comparison 
of the new techniques with the standard procedure of
numerically integrating a matrix Riccati equation 
to determine a feedback matrix.  The new technique is
shown to be significantly faster for comparable 
accuracy.

CACM June, 1971

Bosarge Jr., W. E.
Johnson, O. G.

splines, regulator problem, control theory, numerical analysis

5.1

CA710604 JB February 3, 1978  10:12 AM

2186	5	2186
2186	5	2186
2186	5	2186