PROPT Bryson Maxrange - Revision history

Per at 08:55, 14 February 2012

2012-02-14T08:55:34Z

← Older revision		Revision as of 03:55, 14 February 2012
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	[[File:brysonMaxrange_01.png]]		[[File:brysonMaxrange_01.png]]

			[[Category:PROPT Examples]]

Mbot at 13:04, 8 November 2011

2011-11-08T13:04:08Z

← Older revision		Revision as of 08:04, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: lpcon		Problem type appears to be: lpcon
	Time for symbolic processing: 0.~~11626~~ seconds		Time for symbolic processing: 0.11045 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 1 ConstrEv 55 ConJacEv 55 Iter 34 MinorIter 185		FuncEv 1 ConstrEv 55 ConJacEv 55 Iter 34 MinorIter 185
	CPU time: 0.~~202801~~ sec. Elapsed time: 0.~~197000~~ sec.		CPU time: 0.187201 sec. Elapsed time: 0.192000 sec.

	</pre>		</pre>

Mbot at 18:22, 2 November 2011

2011-11-02T18:22:29Z

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	{{Part Of Manual\|title=the PROPT Manual\|link=[[PROPT \|PROPT Manual]]}}		{{Part Of Manual\|title=the PROPT Manual\|link=[[PROPT\|PROPT Manual]]}}

	==Problem description==		==Problem description==
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	title('Bryson MaxRange control');		title('Bryson MaxRange control');
	</source>		</source>

			[[File:brysonMaxrange_01.png]]

Mbot: Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} ==Problem description== Max range version of Bryson-Denham problem % Copyright ..."

2011-11-02T14:54:30Z

Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} ==Problem description== Max range version of Bryson-Denham problem <source lang="matlab"> % Copyright ..."

New page

{{Part Of Manual|title=the PROPT Manual|link=[[PROPT |PROPT Manual]]}}

==Problem description==

Max range version of Bryson-Denham problem

<source lang="matlab">
% Copyright (c) 2007-2008 by Tomlab Optimization Inc.
</source>

==Problem setup==

<source lang="matlab">
toms t
p = tomPhase('p', t, 0, 2, 50);
setPhase(p);

tomStates x y v
tomControls u1 u2

% Various constants and expressions
xmin = -10; xmax = 10;
ymin = xmin; ymax = xmax;
Vmin = -100; Vmax = 100;
g = 1;
a = 0.5*g;

% Initial guess
x0 = collocate({u1 == 1; u2 == 0});

% Box constraints
cbox = {xmin <= icollocate(x) <= xmax
ymin <= icollocate(y) <= ymax
Vmin <= icollocate(v) <= Vmax
-100 <= collocate(u1) <= 100
-100 <= collocate(u2) <= 100};

% Boundary constraints
cbnd = {initial({x == 0; y == 0; v == 0})
final(y == 0.1)};

% ODEs and path constraints
ceq = {collocate({
dot(x) == v.*u1
dot(y) == v.*u2
dot(v) == a-g*u2
})
collocate(u1.^2+u2.^2 == 1)};

% Objective
objective = -final(x);
</source>

==Solve the problem==

<source lang="matlab">
options = struct;
options.name = 'Bryson MaxRange';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
t = subs(collocate(t),solution);
x = subs(collocate(x),solution);
y = subs(collocate(y),solution);
v = subs(collocate(v),solution);
u1 = subs(collocate(u1),solution);
u2 = subs(collocate(u2),solution);
</source>

<pre>
Problem type appears to be: lpcon
Time for symbolic processing: 0.11626 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Bryson MaxRange f_k -1.712314875015308500
sum(|constr|) 0.000000100745006408
f(x_k) + sum(|constr|) -1.712314774270302200
f(x_0) 0.000000000000000000

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

FuncEv 1 ConstrEv 55 ConJacEv 55 Iter 34 MinorIter 185
CPU time: 0.202801 sec. Elapsed time: 0.197000 sec.

</pre>

==Plot result==

<source lang="matlab">
subplot(2,1,1)
plot(t,x,'*-',t,y,'*-',t,v,'*-');
legend('x','y','v');
title('Bryson MaxRange state variables');

subplot(2,1,2)
plot(t,u1,'+-',t,u2,'+-');
legend('u1','u2');
title('Bryson MaxRange control');
</source>