PROPT Continuous State Constraint Problem - Revision history

Per: /* Plot result */

2012-02-14T08:57:13Z

Plot result

← Older revision		Revision as of 03:57, 14 February 2012
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	[[File:contStateConstraint_01.png]]		[[File:contStateConstraint_01.png]]

			[[Category:PROPT Examples]]

Mbot at 12:07, 9 November 2011

2011-11-09T12:07:18Z

← Older revision		Revision as of 07:07, 9 November 2011
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	<math> J = \int_0^1 x_1(t)^2 + x_2(t)^2 + 0.005*u(t)^2 \mathrm{d}t </math>		<math> J = \int_0^1 x_1(t)^2 + x_2(t)^2 + 0.005*u(t)^2 \mathrm{d}t </math>


	subject to:		subject to:

	<math> \frac{dx_1}{dt} = x_2 </math>		<math> \frac{dx_1}{dt} = x_2 </math>

	<math> \frac{dx_2}{dt} = -x_2+u </math>		<math> \frac{dx_2}{dt} = -x_2+u </math>

	<math> x_1(0) = 0 </math>		<math> x_1(0) = 0 </math>

	<math> x_2(0) = -1 </math>		<math> x_2(0) = -1 </math>

	<math> 8*(t-0.5)^2 - 0.5 - x_2 >=0 </math>		<math> 8*(t-0.5)^2 - 0.5 - x_2 >=0 </math>


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

Mbot at 13:04, 8 November 2011

2011-11-08T13:04:32Z

← Older revision		Revision as of 08:04, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: qp		Problem type appears to be: qp
	Time for symbolic processing: 0.~~078296~~ seconds		Time for symbolic processing: 0.066489 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 10 GradEv 10 ConstrEv 10 Iter 10		FuncEv 10 GradEv 10 ConstrEv 10 Iter 10
	~~CPU time: 0.062400 sec.~~ Elapsed time: 0.~~370000~~ sec.		Elapsed time: 0.007000 sec.

	</pre>		</pre>

Mbot at 18:22, 2 November 2011

2011-11-02T18:22:45Z

← 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 2: Miser3 manual		Problem 2: Miser3 manual
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	title('Cont State Constraint path constraint');		title('Cont State Constraint path constraint');
	</source>		</source>

			[[File:contStateConstraint_01.png]]

Mbot: Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Problem 2: Miser3 manual ==Problem description== Find u(t) over t in [0; 1 ] to minimize $J = \..."$

2011-11-02T14:54:37Z

Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Problem 2: Miser3 manual ==Problem description== Find u(t) over t in [0; 1 ] to minimize <math> J = \..."

New page

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

Problem 2: Miser3 manual

==Problem description==

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

<math> J = \int_0^1 x_1(t)^2 + x_2(t)^2 + 0.005*u(t)^2 \mathrm{d}t </math>

subject to:

<math> \frac{dx_1}{dt} = x_2 </math>
<math> \frac{dx_2}{dt} = -x_2+u </math>
<math> x_1(0) = 0 </math>
<math> x_2(0) = -1 </math>
<math> 8*(t-0.5)^2 - 0.5 - x_2 >=0 </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, 50);
setPhase(p);

tomStates x1 x2
tomControls u

% Initial guess
x0 = {icollocate({x1 == 0; x2 == -1})
collocate(u==0)};

% Box constraints
cbox = {-10 <= icollocate(x1) <= 10
-10 <= icollocate(x2) <= 10
-20 <= collocate(u) <= 20};

% Boundary constraints
cbnd = initial({x1 == 0; x2 == -1});

% ODEs and path constraints
ceq = collocate({
dot(x1) == x2
dot(x2) == -x2+u
8*(t-0.5).^2-0.5-x2 >= 0 % Path constr.
});

% Objective
objective = integrate(x1.^2 + x2.^2 + 0.005*u.^2);
</source>

==Solve the problem==

<source lang="matlab">
options = struct;
options.name = 'Cont State Constraint';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);
t = subs(collocate(t),solution);
x1 = subs(collocate(x1),solution);
x2 = subs(collocate(x2),solution);
u = subs(collocate(u),solution);
</source>

<pre>
Problem type appears to be: qp
Time for symbolic processing: 0.078296 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: 1: Cont State Constraint f_k 0.169824305998485000
sum(|constr|) 0.000000000079762962
f(x_k) + sum(|constr|) 0.169824306078247970
f(x_0) 0.000000000000000000

Solver: CPLEX. EXIT=0. INFORM=1.
CPLEX Barrier QP solver
Optimal solution found

FuncEv 10 GradEv 10 ConstrEv 10 Iter 10
CPU time: 0.062400 sec. Elapsed time: 0.370000 sec.

</pre>

==Plot result==

<source lang="matlab">
subplot(3,1,1)
plot(t,x1,'*-',t,x2,'*-');
legend('x1','x2');
title('Cont State Constraint state variables');

subplot(3,1,2)
plot(t,u,'+-');
legend('u');
title('Cont State Constraint control');

subplot(3,1,3)
ieq = 8*(t-0.5).^2-0.5-x2;
plot(t,ieq,'+-');
axis([0 1 0 5]);
legend('path');
title('Cont State Constraint path constraint');
</source>

PROPT Continuous State Constraint Problem - Revision history

Per: /* Plot result */

Mbot at 12:07, 9 November 2011

Mbot at 13:04, 8 November 2011

Mbot at 18:22, 2 November 2011

Mbot: Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Problem 2: Miser3 manual ==Problem description== Find u(t) over t in [0; 1 ] to minimize J = \..."

Mbot: Created page with "{{Part Of Manual|title=the PROPT Manual|link=PROPT Manual}} Problem 2: Miser3 manual ==Problem description== Find u(t) over t in [0; 1 ] to minimize $J = \..."$