View source for Lotka Volterra fishing problem (ACADO)

This pages states the code to solve the (ralaxed) [[Lotka Volterra fishing problem]] with the code generation fo the ACADO Toolkit from Matlab (via Matlab interface). Hence one needs Matlab and ACADO.
The m-file should be located in the matlab interface of ACADO and the path <ACADOROOT>/interfaces/matlab/examples/codegeneratio/nmpc/. While we use the NMPC more precisely the RTI capability of
the ACADO codegeneration, this features are misused to implement a 20 step SQP solver without stopping criteria.

== ACADO (Matlab) ==

The source code for a fixed grid discretisation with fixed stepsize integrator. This is an m-file that should be called from Matlab AFTER
calling make from matlab in the matlab interface of ACADO.

<source lang="Matlab">

% implements the lotka volterra fishing problem on mintoc.de

clc;
clear all;
close all;

Ts = 0.1;
EXPORT = 1;

%% Variables
DifferentialState x0 x1;
Control w;

n_XD = length(diffStates);
n_U = length(controls);

% Constants
c0 = 0.4;
c1 = 0.2;

%% Differential Equation

f = dot([x0; x1]) == [ x0-x0*x1-c0*x0*w; ...
    -x1 + x0*x1-c1*x1*w];

h = [diffStates];
hN = [diffStates];



%% MPCexport
acadoSet('problemname', 'mpc');

N = 200;
ocp = acado.OCP( 0.0, 12, N );

W_mat = eye(n_XD,n_XD);
WN_mat = eye(n_XD,n_XD);
W = acado.BMatrix(W_mat);
WN = acado.BMatrix(WN_mat);

ocp.minimizeLSQ( W, h );
ocp.minimizeLSQEndTerm( WN, hN );

ocp.subjectTo( 0 <= w <= 1 );
ocp.setModel(f);

mpc = acado.OCPexport( ocp );
mpc.set( 'HESSIAN_APPROXIMATION',       'GAUSS_NEWTON'      );
mpc.set( 'DISCRETIZATION_TYPE',         'MULTIPLE_SHOOTING' );
mpc.set( 'SPARSE_QP_SOLUTION',          'FULL_CONDENSING_N2');
mpc.set( 'INTEGRATOR_TYPE',             'INT_IRK_GL4'       );
mpc.set( 'NUM_INTEGRATOR_STEPS',        N                 );
mpc.set( 'QP_SOLVER',                   'QP_QPOASES'    	);
mpc.set( 'HOTSTART_QP',                 'NO'             	);
mpc.set( 'LEVENBERG_MARQUARDT', 		 1e-10				);

if EXPORT
    mpc.exportCode( 'export_MPC' );
    copyfile('../../../../../../external_packages/qpoases', 'export_MPC/qpoases')
    
    cd export_MPC
    make_acado_solver('../acado_MPCstep')
    cd ..
end

%% PARAMETERS OPTIMIZATION
X0 = [0.5 0.7];
input.x0=X0';
Xref = [1 1];
input.x = repmat(Xref,N+1,1);
Xref = repmat(Xref,N,1);
input.od = [];

Uref = zeros(N,n_U);
input.u = Uref;

input.y = [Xref(1:N,:)];
input.yN = Xref(N,:).';

input.W = diag([1 1]);
input.WN = diag([1 1]);

%% SOLVER LOOP
display('------------------------------------------------------------------')
display('               SOLVER Loop'                                    )
display('------------------------------------------------------------------')



for i=1:20
    tic
    % Solve NMPC OCP
    output = acado_MPCstep(input);
    
    input.x=output.x;
    input.u=output.u;

    disp([' (RTI step: ' num2str(output.info.cpuTime*1e6) ' µs)'])

end


%% PLOT RESULTS

t_end = 12;

% States
figure(1)
plot([0:t_end/N:t_end],output.x)
ylabel('States')
xlabel('Time')
legend('x1','x2')

% Control
figure(2)
plot([0:t_end/N:t_end-t_end/N],output.u)
ylabel('Control (u)')
xlabel('Time')

</source>
[[Category:ACADO]]