Bryson-Denham Problem (Short version)

Contents

Problem description

The Bryson-Denham Problem but we take advantage of the propt input format to compute the cost function directly, without going via u and x3.

% Copyright (c) 2007-2008 by Tomlab Optimization Inc.

Problem setup

toms t tf
p = tomPhase('p', t, 0, tf, 30); setPhase(p);
tomStates x1 x2
x1max = 1/9; x0 = {tf == 0.5};

constr = {0.001 <= tf <= 50
    collocate({0 <= x1 <= x1max; -10 <= x2 <= 10})
    initial({x1 == 0; x2 == 1}); final({x1 == 0; x2 == -1})
    collocate(dot(x1) == x2)};

options = struct;
options.name = 'Bryson Denham Short';
solution = ezsolve(integrate(0.5*dot(x2).^2), constr, x0, options);
t  = subs(collocate(t),solution);
x1 = subs(collocate(x1),solution); x2 = subs(collocate(x2),solution);
figure(1)
plot(t,x1,'*-',t,x2,'*-');
legend('x1','x2');
title('Bryson Denham Short state variables');

Problem type appears to be: con
===== * * * =================================================================== * * *
TOMLAB - Tomlab Optimization Inc. Development license  999001. Valid to 2010-02-05
=====================================================================================
Problem: ---  1: Bryson Denham Short            f_k       3.975295744665011900
                                       sum(|constr|)      0.000000002213305771
                              f(x_k) + sum(|constr|)      3.975295746878317900
                                              f(x_0)   1859.999999999970900000

Solver: snopt.  EXIT=0.  INFORM=1.
SNOPT 7.2-5 NLP code
Optimality conditions satisfied

FuncEv  139 GradEv  137 ConstrEv  137 ConJacEv  137 Iter  136 MinorIter  413
CPU time: 0.328125 sec. Elapsed time: 0.328000 sec.