FelixMueller at 17:52, 31 January 2016

2016-01-31T17:52:32Z

← Older revision		Revision as of 17:52, 31 January 2016
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			Below you can find the MATLAB file that was used in [[:Category: TomDyn/PROPT \| TomDyn/PROPT]] to create the reference solution and its plot for the [[Lotka Volterra fishing problem]].


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

MaxWolff at 15:50, 19 January 2016

2016-01-19T15:50:49Z

← Older revision		Revision as of 15:50, 19 January 2016
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	<source lang="matlab">		<source lang="matlab">

	%% Lotka-Volterra fishing example		%% Lotka-Volterra fishing example (relaxed version)
	%		%
	% Implemented by: Maximilian von Wolff		% Implemented by: Maximilian von Wolff

MaxWolff at 15:50, 19 January 2016

2016-01-19T15:50:32Z

← Older revision		Revision as of 15:50, 19 January 2016
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	setPhase(p);		setPhase(p);
	tomStates x1 x2 x3		tomStates x1 x2 x3
	tomControls u%integer u		tomControls u %or use integer u and set problem type as MINLP and solver as KNITRO as in annotation below

	%initial states		%initial states

MaxWolff: Created page with " %% Lotka-Volterra fishing example % % Implemented by: Maximilian von Wolff % % %% Problem Description % % As on https://modest.math.uni-magdeburg.de/mi..."

2016-01-19T15:48:28Z

Created page with "<source lang="matlab"> %% Lotka-Volterra fishing example % % Implemented by: Maximilian von Wolff % % %% Problem Description % % As on https://modest.math.uni-magdeburg.de/mi..."

New page

<source lang="matlab">

%% Lotka-Volterra fishing example
%
% Implemented by: Maximilian von Wolff
%
%
%% Problem Description
%
% As on https://modest.math.uni-magdeburg.de/mintoc/index.php/Lotka_Volterra_fishing_problem
%
% \min\limits_{x,u} x_3(t_f)
%
% subject to:
%
% dot(x)_1(t) = x_1(t) - x_1(t)*x_2(t) - c_0*x_1(t)*u(t),
% dot(x)_2(t) = -x_2(t) + x_1(t)*x_2(t) - c_1*x_2(t)*u(t),
% dot(x)_3(t) = (x_1(t) - 1)^2 + (x_2(t) - 1)^2,
%
% initial conditions:
%
% x(0)=[0.5, 0.7, 0]'
%
% control constraints:
%
% u(t) \in \{0, 1\} \forall t \in [t_0, t_f]
%
% Parameters
%
% [t_0, t_f] = [0, 12]
% [c_0, c_1] = [0.4, 0.2]
%
%
%
%
%
%% Problem setup
%
% Setup parameters:
%
n = 400;
%

toms t
p = tomPhase('p', t, 0, 12, n);
setPhase(p);
tomStates x1 x2 x3
tomControls u%integer u

%initial states
xi = [0.5, 0.7, 0];

%initial guess
x0 = {collocate(u == 0)
icollocate({x1 == xi(1)
x2 == xi(2)
x3 == xi(3)
})};

%Box constraints
cbox = {(0 <= collocate(u) <= 1)};

%Boundary constraints
cbnd = {initial({ x1 == xi(1);
x2 == xi(2);
x3 == xi(3);})};

%Parameters for ODE's
c = [0.4, 0.2]';
c0 = c(1);
c1 = c(2);

%ODE's

dx1 = x1 - x1.*x2 -c0*x1.*u;
dx2 = -x2 + x1.*x2 - c1*x2.*u;
dx3 = (x1 - 1).^2 + (x2 - 1).^2;

ceq = collocate({
dot(x1) == dx1
dot(x2) == dx2
dot(x3) == dx3});

%Objective

objective = final(x3);

%% Solve the problem
options = struct;
options.name = 'Lotka-Volterra';
%options.type = 'minlp';
%options.solver = 'knitro';
solution = ezsolve(objective, {cbox, cbnd, ceq}, x0, options);

xopt1 = subs(x1,solution);
xopt2 = subs(x2,solution);
xopt3 = subs(x3,solution);
uopt = subs(u,solution);

%Plotting solution

figure(1)
subplot(3,1,1);
ezplot([x1; x2]); legend('Prey','Predator');
xlabel('time');
ylabel('Biomass');
title('Biomasses');

subplot(3,1,2);
ezplot(u); legend('u');
xlabel('time');
ylabel('Control');
title('Fishing control');

subplot(3,1,3);
ezplot(x3); legend('Obj. Value');
xlabel('time');
title('Objective');

disp('Objective Function Value');
disp(final(xopt3));

</source>

[[Category:TomDyn/PROPT]]

Lotka Volterra fishing problem (TomDyn/PROPT) - Revision history

FelixMueller at 17:52, 31 January 2016

MaxWolff at 15:50, 19 January 2016

MaxWolff at 15:50, 19 January 2016

MaxWolff: Created page with " %% Lotka-Volterra fishing example % % Implemented by: Maximilian von Wolff % % %% Problem Description % % As on https://modest.math.uni-magdeburg.de/mi..."