PROPT Global Dynamic System - Revision history

Per: /* Plot result */

2012-02-14T09:03:35Z

Plot result

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	[[File:globalDynamicSystem_01.png]]		[[File:globalDynamicSystem_01.png]]

			[[Category:PROPT Examples]]

Mbot at 12:08, 9 November 2011

2011-11-09T12:08:34Z

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	<math> J = -x^2(t_f) </math>		<math> J = -x^2(t_f) </math>


	subject to:		subject to:

	<math> \frac{dx}{dt} = -x^2+u </math>		<math> \frac{dx}{dt} = -x^2+u </math>

	<math> x(t_0) = 9 </math>		<math> x(t_0) = 9 </math>

	<math> -5 <= u <= 5 </math>		<math> -5 <= u <= 5 </math>


	<source lang="matlab">		<source lang="matlab">

Mbot at 13:05, 8 November 2011

2011-11-08T13:05:34Z

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	TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31		TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
	=====================================================================================		=====================================================================================
	Problem: --- 1: Global Dynamic System - Trial 10 f_k -8.~~232621699201999400~~		Problem: --- 1: Global Dynamic System - Trial 16 f_k -8.232621699200782600
	sum(\|constr\|) 0.~~000000000001198153~~		sum(\|constr\|) 0.000000000019587887
	f(x_k) + sum(\|constr\|) -8.~~232621699200802100~~		f(x_k) + sum(\|constr\|) -8.232621699181194700

	Solver: multiMin with local solver snopt. EXIT=0. INFORM=0.		Solver: multiMin with local solver snopt. EXIT=0. INFORM=0.
	Find local optima using multistart local search		Find local optima using multistart local search
	Did 20 local tries. Found 1 global, 2 minima. TotFuncEv ~~930~~. TotConstrEv ~~890~~		Did 20 local tries. Found 1 global, 2 minima. TotFuncEv 822. TotConstrEv 782

	FuncEv ~~930~~ GradEv ~~890~~ ConstrEv ~~890~~ ConJacEv 30 Iter ~~483~~		FuncEv 822 GradEv 782 ConstrEv 782 ConJacEv 35 Iter 482
	CPU time: 0.~~561604~~ sec. Elapsed time: 0.~~531000~~ sec.		CPU time: 0.452403 sec. Elapsed time: 0.451000 sec.

	</pre>		</pre>

Mbot at 18:23, 2 November 2011

2011-11-02T18:23:27Z

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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]]}}

	Deterministic Global Optimization of Nonlinear Dynamic Systems, Youdong Lin and Mark A. Stadtherr, Department of Chemical and Biomolecular Engineering, University of Notre Dame		Deterministic Global Optimization of Nonlinear Dynamic Systems, Youdong Lin and Mark A. Stadtherr, Department of Chemical and Biomolecular Engineering, University of Notre Dame
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	legend('u');		legend('u');
	</source>		</source>

			[[File:globalDynamicSystem_01.png]]

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Deterministic Global Optimization of Nonlinear Dynamic Systems, Youdong Lin and Mark A. Stadtherr, Department of Chemical and Biomolecular Engineering, University of Notre Dame

==Problem Description==

Find u over t in [0; 1 ] to minimize:

<math> J = -x^2(t_f) </math>

subject to:

<math> \frac{dx}{dt} = -x^2+u </math>
<math> x(t_0) = 9 </math>
<math> -5 <= u <= 5 </math>

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

==Problem setup==

<source lang="matlab">
toms t
p = tomPhase('p', t, 0, 1, 20);
setPhase(p);

tomStates x
tomControls u

% Box constraints, bounds and odo
c = {-10 <= icollocate(x) <= 10
-5 <= collocate(u) <= 5
initial(x == 9)
collocate(dot(x) == -x.^2+u)};
</source>

==Solve the problem==

<source lang="matlab">
options = struct;
options.name = 'Global Dynamic System';
Prob = sym2prob('con',-final(x)^2, c, [], options);
Prob.xInit = 20;
Result = tomRun('multiMin', Prob, 1);
solution = getSolution(Result);
t = subs(collocate(t),solution);
x = subs(collocate(x),solution);
u = subs(collocate(u),solution);
</source>

<pre>
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Global Dynamic System - Trial 10 f_k -8.232621699201999400
sum(|constr|) 0.000000000001198153
f(x_k) + sum(|constr|) -8.232621699200802100

Solver: multiMin with local solver snopt. EXIT=0. INFORM=0.
Find local optima using multistart local search
Did 20 local tries. Found 1 global, 2 minima. TotFuncEv 930. TotConstrEv 890

FuncEv 930 GradEv 890 ConstrEv 890 ConJacEv 30 Iter 483
CPU time: 0.561604 sec. Elapsed time: 0.531000 sec.

</pre>

==Plot result==

<source lang="matlab">
figure(1);
subplot(2,1,1);
plot(t,x,'*-');
legend('x');

subplot(2,1,2);
plot(t,u,'*-');
legend('u');
</source>