PROPT Bryson-Denham Problem - Revision history

Per at 08:54, 14 February 2012

2012-02-14T08:54:53Z

← Older revision		Revision as of 03:54, 14 February 2012
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	[[File:brysonDenham_01.png]]		[[File:brysonDenham_01.png]]

			[[Category:PROPT Examples]]

Mbot at 13:03, 8 November 2011

2011-11-08T13:03:55Z

← Older revision		Revision as of 08:03, 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.~~13757~~ seconds		Time for symbolic processing: 0.1271 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 1 ConstrEv 63 ConJacEv 63 Iter 60 MinorIter 260		FuncEv 1 ConstrEv 63 ConJacEv 63 Iter 60 MinorIter 260
	CPU time: 0.343202 sec. Elapsed time: 0.~~354000~~ sec.		CPU time: 0.343202 sec. Elapsed time: 0.336000 sec.

	</pre>		</pre>

Mbot at 18:22, 2 November 2011

2011-11-02T18:22:20Z

← Older revision		Revision as of 13:22, 2 November 2011
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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 Denham control');		title('Bryson Denham control');
	</source>		</source>

			[[File:brysonDenham_01.png]]

Mbot at 14:54, 2 November 2011

2011-11-02T14:54:24Z

← Older revision		Revision as of 09:54, 2 November 2011
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			{{Part Of Manual\|title=the PROPT Manual\|link=[[PROPT \|PROPT Manual]]}}

	==Problem description==		==Problem description==
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	Standard formulation for Bryson-Denham		Standard formulation for Bryson-Denham

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

	==Problem setup==		==Problem setup==

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	setPhase([]);		setPhase([]);

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	p = tomPhase('p', t, 0, t_f, 50);		p = tomPhase('p', t, 0, t_f, 50);
	</~~syntaxhighlight~~>		</source>

	==Solve the problem==		==Solve the problem==

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	options = struct;		options = struct;
	options.name = 'Bryson Denham';		options.name = 'Bryson Denham';
	options.phase = p;		options.phase = p;
	solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);		solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
	</~~syntaxhighlight~~>		</source>

	<pre>		<pre>
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	==Plot result==		==Plot result==

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	subplot(2,1,1)		subplot(2,1,1)
	ezplot(subs(docollocate(p,[x1 x2 x3]),solution),0,solution.t_f);		ezplot(subs(docollocate(p,[x1 x2 x3]),solution),0,solution.t_f);
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	legend('u');		legend('u');
	title('Bryson Denham control');		title('Bryson Denham control');
	</~~syntaxhighlight~~>		</source>

Mbot: Created page with " ==Problem description== Standard formulation for Bryson-Denham % Copyright (c) 2007-2008 by Tomlab Optimization Inc. ==Prob..."

2011-11-02T11:42:07Z

New page

==Problem description==

Standard formulation for Bryson-Denham

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

==Problem setup==

<syntaxhighlight lang="matlab">
setPhase([]);

toms t t_f

x10 = 0; x20 = 1;
x30 = 0; x1f = 0; x2f = -1;
x1min = -10; x1max = 10; x2min = x1min;
x2max = x1max; x3min = x1min; x3max = x1max;

tomStates x1 x2 x3
tomControls u

% Initial guess
x0 = {t_f == 0.5
icollocate({
x1 == x10+(x1f-x10)*t/t_f
x2 == x20+(x2f-x20)*t/t_f
x3 == x30
})
collocate(u==0)};

% Box constraints
cbox = {0.001 <= t_f <= 50
0 <= mcollocate(x1) <= 1/9
x2min <= mcollocate(x2) <= x2max
x3min <= mcollocate(x3) <= x3max
-5000 <= collocate(u) <= 5000};

% Boundary constraints
cbnd = {initial({x1 == x10; x2 == x20; x3 == x30})
final({x1 == x1f; x2 == x2f})};

% ODEs and path constraints
ceq = collocate({
dot(x1) == x2
dot(x2) == u
dot(x3) == u.^2/2});

% Objective
objective = final(x3);

p = tomPhase('p', t, 0, t_f, 50);
</syntaxhighlight>

==Solve the problem==

<syntaxhighlight lang="matlab">
options = struct;
options.name = 'Bryson Denham';
options.phase = p;
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
</syntaxhighlight>

<pre>
Problem type appears to be: lpcon
Time for symbolic processing: 0.13757 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Bryson Denham f_k 4.000021208621198800
sum(|constr|) 0.000000174861447145
f(x_k) + sum(|constr|) 4.000021383482645900
f(x_0) 0.000000000000000000

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

FuncEv 1 ConstrEv 63 ConJacEv 63 Iter 60 MinorIter 260
CPU time: 0.343202 sec. Elapsed time: 0.354000 sec.

</pre>

==Plot result==

<syntaxhighlight lang="matlab">
subplot(2,1,1)
ezplot(subs(docollocate(p,[x1 x2 x3]),solution),0,solution.t_f);
legend('x1','x2','x3');
title('Bryson Denham state variables');

subplot(2,1,2)
ezplot(subs(docollocate(p,u),solution),0,solution.t_f);
legend('u');
title('Bryson Denham control');
</syntaxhighlight>