FelixMueller at 17:53, 31 January 2016

2016-01-31T17:53:04Z

← Older revision		Revision as of 17:53, 31 January 2016
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			Below you can find the MATLAB file that was used in [[:Category: switch \| switch]] to create the reference solution and its plot for the [[Lotka Volterra fishing problem]].


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

ClemensZeile at 17:46, 19 January 2016

2016-01-19T17:46:59Z

← Older revision		Revision as of 17:46, 19 January 2016
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			<source lang="matlab">

	% Copyright 2014 Mathieu Claeys, http://mathclaeys.wordpress.com/		% Copyright 2014 Mathieu Claeys, http://mathclaeys.wordpress.com/

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	% create/update Bocop directory		% create/update Bocop directory
	%toBocop('initLotka',ocpDef,t,x,u,l,d);		%toBocop('initLotka',ocpDef,t,x,u,l,d);

			</source>
			[[Category:switch]]

ClemensZeile: Created page with "% Copyright 2014 Mathieu Claeys, http://mathclaeys.wordpress.com/ %% Data % Scaling factors: it is essential to scale variables so that everything % falls within a unit box..."

2016-01-19T16:05:54Z

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% Copyright 2014 Mathieu Claeys, http://mathclaeys.wordpress.com/

%% Data

% Scaling factors: it is essential to scale variables so that everything
% falls within a unit box, otherwise moment problem will be poorly scaled
% (Consider moments of the Dirac measure located at 10...)
xscale = 1;
tscale = 12;
%lscale = sqrt(5);

% Relaxation order
order = 5; % Choose order >= 1;

%% Create problem definition structure
ocpDef.nModes = 2;
ocpDef.nStates = 3;
ocpDef.nControls = 0;
ocpDef.nLifts = 0;
ocpDef.scaling.x = [xscale,xscale,xscale];
ocpDef.scaling.t = tscale;
ocpDef.scaling.u = 1;
ocpDef.scaling.l = 1;
ocpDef.dynamics{1} = @(t,x,u,l) [(x(1)-x(1)*x(2)-0.4*x(1))*tscale;
(-x(2)+x(1)*x(2)-0.2*x(2))*tscale;
((x(1)-1)^2+(x(2)-1)^2)*tscale]; %[(1-lscale*l(1))*tscale/xscale;(lscale*l(1)-lscale*l(2))*tscale/xscale];
ocpDef.dynamics{2} = @(t,x,u,l) [(x(1)-x(1)*x(2))*tscale;
(-x(2)+x(1)*x(2))*tscale;
((x(1)-1)^2+(x(2)-1)^2)*tscale];
ocpDef.runningCost{1} = @(t,x,u,l) 0;
ocpDef.runningCost{2} = @(t,x,u,l) 0;
ocpDef.initialCost = @(t,x,l) 0;
ocpDef.terminalCost = @(t,x,l) x(3);
ocpDef.runningConstraints = @(t,x,u,l) [t*(1-t)>=0; % normalized time in [0,1]
x(1) >= 0; % levels are positive
x(2) >= 0;
x(3) >=0;];
% 0==(lscale*l(1))^2-xscale*x(1); %algebraic lifts for square roots
%l(1)>=0;
%0==(lscale*l(2))^2-xscale*x(2);
%l(2)>=0;];
ocpDef.initialConstraints = @(t,x,l) [x(1)==0.5;x(2)==0.7;x(3)==0;t==0];
ocpDef.terminalConstraints = @(t,x,l) [t==1];
% NB: to satisfy Putinar's theorem, there should be for each measure a ball
% constraint on all variables. Ignore this assumption at your own risks.
ocpDef.integralConstraints = {};

%% Construct and solve GloptiPoly problem
% (requires the installation of Yalmip and a SDP solver. We recommend Mosek
% for speed and SeDuMi for accuracy)

% Create GloptiPoly measure objects with default names (NB: resets all
% GloptiPoly states to zero). To impose specific names, construct measures
% by hand.
measureSystem = switchedMeasureSystem(ocpDef);

% Create GloptiPoly msdp object, modeling a given order moment relaxation
P = switchedRelaxation( ocpDef, measureSystem, order );

% Solve GloptiPoly problem
%mset('yalmip',true); % default SDP solver of Yalmip will be called. If
%commented, Yalmip is not called and GloptiPoly looks for SeDuMi.
[status,obj,m] = msol(P);
obj

%% Solution extraction
npoints.t = 80;
npoints.var = 80;
% NB: extract moments of one order less, because higher order moments are
% very unprecise, since they are not constrained enough
[t,x,u,l,d] = extractSolution( ocpDef, measureSystem, order-1, npoints );

figure
plot(t,x,'*-');
xlabel('t');
ylabel('x');
legend('x_1','x_2','x_3');

figure
plot(t,d(:,1),'o-',t,d(:,2),'+-');
xlabel('t');
ylabel('duty cycle');
legend('Mode 1','Mode 2');

% create/update Bocop directory
%toBocop('initLotka',ocpDef,t,x,u,l,d);

Lotka Volterra fishing problem (switch) - Revision history

FelixMueller at 17:53, 31 January 2016

ClemensZeile at 17:46, 19 January 2016

ClemensZeile: Created page with "% Copyright 2014 Mathieu Claeys, http://mathclaeys.wordpress.com/ %% Data % Scaling factors: it is essential to scale variables so that everything % falls within a unit box..."