riccati.m

this file is a zip file for multi objective optimization by matlab.

function [j] = riccati (n, x0)
% Returns the optimal value of the Riccati equation
% for the input parameters n and x0

% By Kerry W. Lothrop <[e-mail]>
%
% Lothrop, K.W.: Conceptual Design Optimization of a Cis-Lunar
% Transportation Architecture Using Genetic Algorithms, Universit鋞
% Stuttgart, University of Colorado, 2003
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 1, or (at your option)
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details. A copy of the GNU 
% General Public License can be obtained from the 
% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.


k = zeros(n, 1);
k(n) = 1;
for i = (n-1):-1:1
    k(i) = 1 + k(i + 1)/(1 + k(i + 1));
end
j = (1 + k(1)/(1 + k(1))) * x0^2;