PROPT Hyper Sensitive Optimal Control: Difference between revisions
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[[Category:PROPT Examples]] |
Latest revision as of 05:05, 14 February 2012
This page is part of the PROPT Manual. See PROPT Manual. |
Eigenvector approximate dichotomic basis method for solving hyper-sensitive optimal control problems 2000, Anil V. Rao and Kenneth D. Mease
3.1. Motivating example, a hyper-sensitive HBVP
Problem Formulation
Find u(t) over t in [0; t_f ] to minimize
subject to:
% Copyright (c) 2007-2008 by Tomlab Optimization Inc.
Problem setup
toms t
p = tomPhase('p', t, 0, 10, 50);
setPhase(p);
tomStates x
tomControls u
% Initial guess
x0 = {icollocate(x == 0)
collocate(u == 0)};
% bounds and ODEs
bceq = {collocate(dot(x) == -x.^3+u)
initial(x) == 1; final(x) == 1.5};
% Objective
objective = integrate(x.^2+u.^2);
Solve the problem
options = struct;
options.name = 'Hyper Sensitive';
solution = ezsolve(objective, bceq, x0, options);
t = subs(collocate(t),solution);
x = subs(collocate(x),solution);
u = subs(collocate(u),solution);
Problem type appears to be: qpcon Time for symbolic processing: 0.080469 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Hyper Sensitive f_k 6.723925391388339900 sum(|constr|) 0.000000002440693436 f(x_k) + sum(|constr|) 6.723925393829033800 f(x_0) 0.000000000000000000 Solver: snopt. EXIT=0. INFORM=1. SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 ConstrEv 26 ConJacEv 26 Iter 21 MinorIter 70 CPU time: 0.031200 sec. Elapsed time: 0.031000 sec.
Plot result
subplot(2,1,1)
plot(t,x,'*-');
legend('x');
title('Hyper Sensitive state variables');
subplot(2,1,2)
plot(t,u,'+-');
legend('u');
title('Hyper Sensitive control');