Network with 100 unstable nodes

% An example from Motee and Jadbabaie,
% "Optimal control of spatially distributed systems",
% IEEE Trans. Automat. Control,
% vol. 53, no. 7, pp. 1616–1629, 2008.

% N nodes randomly distributed in a box [0 L] x [0 L]
N = 100;
L = 10;

load data/positions
% or generate the random distribution of the nodes
% pos = L*rand(N,2);

% the state-space representation of subsystem i
Aii = [1 1; 1 2];
Bii = [0; 1];
n   = size(Bii,1);
Aij = eye(n);

B1  = kron(eye(N), Bii);
B2  = B1;

% construct
% (a) the Euclidean distance matrix that describes the distance
% between two systems i and j
% (b) the A-matrix of the distributed system

A = zeros(2*N,2*N);
dismat = zeros(N,N);
for i = 1:N
    for j = i:N
        if i == j
            A( (i-1)*n + 1 : i*n, (j-1)*n + 1 : j*n ) = Aii;
        else
            dismat(i,j) = sqrt( norm( pos(i,:) - pos(j,:) )^2 );
            dismat(j,i) = dismat(i,j);
            A( (i-1)*n + 1 : i*n, (j-1)*n + 1 : j*n ) = Aij / exp( dismat(i,j) );
            A( (j-1)*n + 1 : j*n, (i-1)*n + 1 : i*n ) = Aij / exp( dismat(j,i) );
        end
    end
end

% state and control penalty weights
Q = eye(2*N);
R = eye(N);

% compute sparse feedback gains
options = struct('method','wl1','gamval',logspace(-2,log10(68.6649),48), ...
        'rho',100,'maxiter',10,'blksize',[1 1],'reweightedIter',1);

tic
solpath = lqrsp(A,B1,B2,Q,R,options);
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