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Commit 3b326199 authored by Venkatraman Renganathan's avatar Venkatraman Renganathan
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Delete CheckAndersLMI.m

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This code simulates distributed minimax adaptive control algorithm for
% uncertain networked systems.
%
% Copyrights Authors: 1) Venkatraman Renganathan - Lund University, Sweden.
% 2) Anders Rantzer - Lund University, Sweden.
% 3) Olle Kjellqvist - Lund University, Sweden.
%
% Email: venkatraman.renganathan@control.lth.se
% anders.rantzer@control.lth.se
% olle.kjellqvist@control.lth.se
%
% Date last updated: 20 October, 2023.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Make a fresh start
clear all; close all; clc;
% set properties for plotting
set(groot,'defaultAxesTickLabelInterpreter','latex');
set(groot,'defaulttextinterpreter','latex');
set(groot,'defaultLegendInterpreter','latex');
% Flag deciding whether to generate new data or load existing data
% dataPrepFlag = 1: Generates new network data
% dataPrepFlag = 0: Loads existing network data
dataPrepFlag = 1;
% When dataPrepFlag = 1: Generate new data for network
if(dataPrepFlag)
disp('Generating new data for network as dataPrepFlag = 1.');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Define the network data using graph structure
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Specify Number of nodes
N = 6;
% Specify Number of edges
M = N - 1;
% Create a random graph with N nodes and M edges
[adjMatrix, I, graphVariable] = GenerateRandomTreeGraph(N);
% Get number of edges on graph
numEdges = size(graphVariable.Edges.EndNodes, 1);
fprintf('Generated random graph is acyclic and has only one component \n');
% Plot the graph - large graph can be time consuming & may not be informative
if N <= 300
plot(graphVariable);
else
disp('The graph is too large to display.');
end
% Infer state and input dimensions
[n,m] = size(I);
% Get the degree vector
degreeVec = sum(adjMatrix, 1)';
% Get one of the node indeces with maximum degree for plotting
[~, maxDegreeNodeIndex] = max(degreeVec);
% Form input matrix B with parameter b and matrix I such that B/b = I
b = 0.1;
B = b*I;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Prepare the dynamics matrix A for each Model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Specify the number of possible plant network parameters
numModels = 2;
% Populate all the possible plant models
for dIter = 1:numModels
% Placeholders for a matrix for each component
ai = zeros(n, 1);
% Flag for stopping while loop
dynamicsPreparationFlag = 1;
% Counter for populating ai vector
iter = 1;
% Loop through until ai^2 + bb^{T} < ai is satisfied
while dynamicsPreparationFlag
% Generate a random ai
ai(iter, 1) = rand;
% Check condition
if(ai(iter, 1)^2 - ai(iter, 1) + 2*b^2*degreeVec(iter, 1) < 0)
iter = iter + 1;
end
% if counter exceeds limit, form the A matrix & stop while loop
if(iter > n)
A = diag(ai);
dynamicsPreparationFlag = 0;
end
end
% Prepare A and B matrices
AMatrices{dIter} = A;
BMatrices{dIter} = B;
end
AVector = zeros(n, numModels);
for dIter = 1:numModels
AVector(:, dIter) = diag(AMatrices{dIter});
end
Arowvectors = {};
for i = 1:N
Arowvectors{i} = AVector(i, :);
end
Acombs = combvec(Arowvectors{:}).';
% Find min & max a values for each node from all possible numModels values
minAVector = min(AVector, [], 2);
maxAVector = max(AVector, [], 2);
% Form the Max A matrix using maxAVector
maxAMatrix = diag(maxAVector);
% Find the network level global minimum and maximum a value
netMinA = min(minAVector);
netMaxA = max(maxAVector);
% Infer the number of possible plants
numPlants = numModels^(N);
% Compute Hinfty control for each possible plants
for i = 1:numPlants
APossibles{i} = diag(Acombs(i, :));
BPossibles{i} = B;
% Compute H_infinity control as u = Kx, with K = B'*(A-I)^{-1}
KinfPossibles{i} = BPossibles{i}'*inv(APossibles{i} - eye(n));
end
disp('Finished Computing H_infinity Control Gains');
% Check Anders LMI for each possible plant
gamma = 7;
P_non = (2/(1 - netMaxA))*eye(n);
P_non_inv = ((1 - netMaxA)/2)*eye(n);
P_wt = inv(P_non_inv - gamma^(-2)*eye(n));
Q = eye(n);
R = eye(M);
happy = 1;
for k = 1:numPlants
Ak = APossibles{k};
if(happy == 0)
break;
end
for l = 1:numPlants
Al = APossibles{l};
if(happy == 0)
break;
end
for p = 1:numPlants
if(happy == 0)
break;
end
if(k ~= l && l == p)
continue;
end
Kp = KinfPossibles{p};
A_cl_kp = Ak + B*Kp;
A_cl_lp = Al + B*Kp;
AndersRHS = Q + Kp'*R*Kp + 0.25*(A_cl_kp+A_cl_lp)'*P_wt*(A_cl_kp+A_cl_lp) - 0.25*gamma^(2)*(A_cl_kp-A_cl_lp)'*(A_cl_kp-A_cl_lp);
AndersLMI = P_non - AndersRHS;
if(all(eig(AndersLMI)) >= 0)
happy = 1;
else
happy = 0;
end
end
end
end
% Finished Checking Anders LMI
if(happy == 1)
disp('Choice of Pkl matrices satisfy Anders LMI.');
else
disp('Choice of Pkl matrices do not satisfy Anders LMI.');
end
% Save the generated network data into mat file.
disp('Saving the generated small network data.');
%save('smallNetworkDynamicsData.mat');
else
disp('Loading existing data for small network as dataPrepFlag = 0.');
%load('smallNetworkDynamicsData.mat');
end
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