PROPT Singular Control 1
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This page is part of the PROPT Manual. See PROPT Manual. |
ITERATIVE DYNAMIC PROGRAMMING, REIN LUUS
10.2.1 Example 1
CHAPMAN & HALL/CRC Monographs and Surveys in Pure and Applied Mathematics
Problem Formulation
Find u over t in [0; 2 ] to minimize
subject to:
The initial condition are:
% Copyright (c) 2007-2008 by Tomlab Optimization Inc.
Problem setup
toms t
p = tomPhase('p', t, 0, 2, 50);
setPhase(p);
tomStates x1 x2
tomControls u
% Initial guess
x0 = {icollocate({x1 == 1; x2 == 0})
collocate(u == 0)};
% Box constraints
cbox = {-1 <= collocate(u) <= 1};
% Boundary constraints
cbnd = initial({x1 == 1; x2 == 0});
% ODEs and path constraints
ceq = collocate({dot(x1) == u
dot(x2) == 0.5*x1.^2});
% Objective
objective = final(x2);
Solve the problem
options = struct;
options.name = 'Singular Control 1';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
t = subs(collocate(t),solution);
u = subs(collocate(u),solution);
Problem type appears to be: lpcon Time for symbolic processing: 0.064118 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Singular Control 1 f_k 0.166665695130345510 sum(|constr|) 0.000000330654862346 f(x_k) + sum(|constr|) 0.166666025785207870 f(x_0) 0.000000000000000000 Solver: snopt. EXIT=0. INFORM=1. SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 ConstrEv 41 ConJacEv 41 Iter 39 MinorIter 164 CPU time: 0.078001 sec. Elapsed time: 0.079000 sec.
Plot result
figure(1)
plot(t,u,'+-');
legend('u');
title('Singular Control 1 control');