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Main_DSP_entropy_2agents_neighbourhood.m
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Main_DSP_entropy_2agents_neighbourhood.m
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%function [ARMSE_f1,ARMSE1] = Main2(BW);
clear classes;
clc;
global g rho_0 Qsqrt Delta M H gamma QPtArray wPtArray nPts;
[QPtArray,wPtArray,nPts] = findSigmaPts(3);
%%%================ Parameter definitions ==================
g = 9.8; % gravity in m/s2
fs = 10; % Sampling rate 10kHz;
fs_ctr = 1; % running freuqncy of ctr; Defining the update frequency of CTR
T = 1/fs;
Delta = T;
rho_0 = 1.754; %prop. constant in air density
gamma = 1.49e-4; %decaying par. in air density
c = 2.999e8; % speed of propagation m/s
fc = 2*pi*10.4e9; % 10.4Ghz X-band radar
tf = 10e-9; % rise/fall time: 10 ns;
r_snr0 = 80e3; % range when snr = 0db; 50km
lmd_min = 10e-6; % min of lambda: 10 mu seconds duration of envelope
lmd_max = 300e-6; % max of lambda: 100 mu seconds
d_lmd = 10e-6; % grid size for lambda
b_min = -300e8; % min of chirp rate: 10,000
b_max = 300e8; % max of chirp rate: 500,000
d_b = 50e8; % grid size for chirp rate
%delta_f = 15e3; % frequency sweep
%BW = Inf; % bandwidth
BW = 8e6;
Lambda = diag([1,1,1]); % weight matrix showing signaficence of state [pos, vel, ball_coef]
seed = 2e5; rand('seed',seed);
%%%============= Parameters for model ==================
q1 = 0.01;
q2 = 0.01;
Q = [q1*Delta^3/3 q1*Delta^2/2 0;
q1*Delta^2/2 q1*Delta 0;
0 0 q2*Delta]; %Process Noise Covariance
Qsqrt = mysqrt(Q);
nExpt = 300; % number of MC runs
t_sim = 5; % simulation time: 30s
N = floor(t_sim/Delta); % number of time steps
M = 30e3; % horizontal distance of the radar to object (km)
H = 30; % radar height (m)
discount = .5; % discount factor in RL
gamma_back = 1; % backward discount factor
lf = 1.0; % Learning factor in RL
lfRL2 = lf;
lfRL3 = lf;
epsilon = 0; % epsilon-greedy (epsilon*100% of times will be random)
epsilonRL2 = epsilon; % epsilon of agent2
epsilonRL3 = epsilon; % epsilon of agent3
window = 10;
numPlanningTrials = 5; % must NOT be greater than number of actions
%%%================ Generate mesh point for [lmd, b] ========
lmd0 = lmd_min : d_lmd : lmd_max;
b0 = [-b_max : d_b : -b_min, b_min : d_b : b_max];
%%pick up the radar parameters that satisfies the bandwidth constraint
para = pick_theta(lmd0,b0,BW);
MSE = zeros(nExpt,3,N);
estMSE = zeros(nExpt,3,N);
MSE_f = zeros(nExpt,3,N);
estMSE_f= zeros(nExpt,3,N);
MSE_RL = zeros(nExpt,3,N);
estMSE_RL= zeros(nExpt,3,N);
fprintf('Grid points %d x %d = %d\n',length(lmd0),length(b0),length(lmd0)*length(b0));
%%%================ Initialize CKF ==========================
time_old = zeros(nExpt,N);
time_new = zeros(nExpt,N); % agent1
time_new2 = zeros(nExpt,N); % agent2
time_new3 = zeros(nExpt,N); % agent3
entropyBank = zeros(nExpt, N); % placeholder for entropies for RL method (agent1)
entropyBank2 = zeros(nExpt, N); % placeholder for entropies for RL method (agent2)
entropyBank3 = zeros(nExpt, N); % placeholder for entropies for RL method (agent2)
entropyBankf = zeros(nExpt, N); % placeholder for entropies for fixed-waveform
for expt = 1:nExpt
countIdx = 0;
%% Fixed waveform selection
wf_fix_idx = fix(rand*length(para) + 1);
lmd_fixed = para(1,wf_fix_idx);
b_fixed = para(2,wf_fix_idx);
% Q-Learning object with 1 state, 764 actions, alpha=.5, gamma=.5, and
% epsilon=0 (which means it is completely greedy):
clear agent;
clear agent2;
clear agent3;
agent = QL(1, 1:764, discount, lf, epsilon);
agent2 = QL(1, 1:764, discount, lfRL2, epsilonRL2);
agent3 = QL(1, 1:764, discount, lfRL3, epsilonRL3);
x = [61e3; 3048; 19161]; %Initial state
xkk = [61.5e3; 3000; 19100];%[62e3; 3400; 19100];
Skk = sqrt(diag([(1e3)^2; (100)^2; 1e4]));
xkk_f = xkk;
Skk_f = Skk;
xkk_RL = xkk;
Skk_RL = Skk;
preEntropy = det(Lambda*(Skk_RL*Skk_RL')); % initial entropy
xkk_RL2 = xkk;
Skk_RL2 = Skk;
preEntropy2 = det(Lambda*(Skk_RL2*Skk_RL2')); % initial entropy
xkk_RL3 = xkk;
Skk_RL3 = Skk;
preEntropy3 = det(Lambda*(Skk_RL3*Skk_RL2')); % initial entropy
fprintf('Monte Carlo runs: %d out of %d\n',expt, nExpt);
%%%==================== Main loop ===========================
for k = 1 : N,
%%% learning coef. update
% agent.alpha = .8;
%%% ========= State and Mst Eqs ========================
x = StateEq(x)+ Qsqrt*randn(3,1);
z_idl = MstEq(x);
%%% ========== Predict ================================
[xkk1,Skk1] = Predict(xkk,Skk);
[xkk1_f,Skk1_f] = Predict(xkk_f,Skk_f);
[xkk1_RL,Skk1_RL] = Predict(xkk_RL,Skk_RL);
[xkk1_RL2,Skk1_RL2] = Predict(xkk_RL2,Skk_RL2);
[xkk1_RL3,Skk1_RL3] = Predict(xkk_RL3,Skk_RL3);
%%%============ Subroutine for fixed waveform =====================
R_f = computeR_FI(c, fc, lmd_fixed, b_fixed, r_snr0, M, xkk1_f(1)-H);
Rsqrt_f = mysqrt(R_f);
z_f = z_idl + Rsqrt_f* randn(2,1);
[xkk_f,Skk_f] = Update(xkk1_f,Skk1_f,z_f,Rsqrt_f);
fEntropy = det(Lambda*(Skk_f*Skk_f'));
entropyBankf(expt,k) = fEntropy;
%%%================================================================
%%% ========== new meas. cov. as per new theta =======
% tic
% if (k==1) || (k<30) || (rem(k,1/(fs_ctr*T))==0),
% for i = 1 : length(para),
% theta = para(:,i)'; % fetch grid point (lmd, b)
% lmd = theta(1);
% b = theta(2);
%
% %%% Calculate measurement covariance: R
% R = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1(1)-H);
% Rsqrt = mysqrt(R);
% %%% Approximate cost function: J(\theta)
% Skk = ComputeSkk(xkk1,Skk1,Rsqrt);% + p_ratio*Skk_p;
%
% J(i)= trace(Lambda*(Skk*Skk'));
% end
% [min_J,idx] = min(J); % find the minimum of J
% lmd = para(1,idx);
% b = para(2,idx);
% wf_lmd(expt, k) = lmd;
% wf_b(expt, k) = b;
% wf_idx(expt,k) = idx;
% end
% %%% Calculate measurement covariance R using new waveform
% R = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1(1)-H);
% Rsqrt = mysqrt(R);
mmm = randn(2,1);
% z = z_idl + Rsqrt*mmm;
% [xkk,Skk] = Update(xkk1,Skk1,z,Rsqrt);
% time_old(expt,k) = toc;
%%%================================================================
%% RL:
% predictedEntropy = zeros(1,length(para)); % init. vector to speed up
% predictedReward = zeros(1,length(para)); % init. vector to speed up
% reward = zeros(1,N);
% tic
% if (k==1) || (k<30) || (rem(k,1/(fs_ctr*T))==0),
% %%%%% Planning %%%%%
tester = randGenerator(numPlanningTrials, length(para));
% for count = 1 : length(tester)%length(para),
% i = tester(count);
% theta = para(:,i)'; % fetch grid point (lmd, b)
% lmd = theta(1);
% b = theta(2);
%
% %%% Calculate measurement covariance: R
% R_RL = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1_RL(1)-H); %%%
% Rsqrt_RL = mysqrt(R_RL); %%%
% Skk_RL = ComputeSkk(xkk1_RL,Skk1_RL,Rsqrt_RL); %%%
% predictedEntropy(count) = det(Lambda*(Skk_RL*Skk_RL'));
% reward_rel = abs(log(abs(preEntropy - predictedEntropy(count))));
% % reward_abs = 1/abs(log(predicted Entropy(count)));
% predictedReward(i) = reward_rel*sign(preEntropy - predictedEntropy(count));
% % learing from prediction
% agent = agent.learning(1,1,i,predictedReward(i)); % there is only one state (1)
% end
%
% %%%%% Learning %%%%%
% % trigering epsilon-greedy action
% idx = agent.egAction(1); % index of eps-greedy action
% if idx == 0 % no learning yet
% idx = fix(rand*length(para) + 1); % random selection
% end
% lmd = para(1,idx);
% b = para(2,idx);
% wf_lmd(expt, k) = lmd;
% wf_b(expt, k) = b;
% wf_idx(expt,k) = idx;
%
% % computing R as the result of the applied action
% R_RL = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1_RL(1)-H); %%%
% Rsqrt_RL = mysqrt(R_RL); %%%
% end
%
% z_RL = z_idl + Rsqrt_RL*mmm; %%%
% [xkk_RL,Skk_RL] = Update(xkk1_RL,Skk1_RL,z_RL,Rsqrt_RL); %%%
%
% % computing the new entropic state
% newEntropy = det(Lambda*(Skk_RL*Skk_RL'));
%
% % computing the reward
% reward_rel = abs(log(abs(preEntropy - newEntropy)));
% reward_abs = 1/abs(log(newEntropy));
% reward(k) = reward_rel*sign(preEntropy - newEntropy);
% % reward(i)
%
% % learning by Q-learning method
% agent = agent.learning(1,1,idx,reward(k)); % there is only one state (1)
%
% % updating the previous entropy
% preEntropy = newEntropy;
% time_new(expt,k) = toc;
% entropyBank(expt,k) = preEntropy;
%%%================================================================
%% RL2:
predictedEntropy2 = zeros(1,length(para)); % init. vector to speed up
predictedReward2 = zeros(1,length(para)); % init. vector to speed up
reward2 = zeros(1,N);
tic
if (k==1) || (k<30) || (rem(k,1/(fs_ctr*T))==0),
%%%%% Planning %%%%%
% tester = randGenerator(numPlanningTrials, length(para));
for count = 1 : length(tester)%length(para),
i = tester(count);
theta = para(:,i)'; % fetch grid point (lmd, b)
lmd = theta(1);
b = theta(2);
%%% Calculate measurement covariance: R
R_RL2 = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1_RL2(1)-H); %%%
Rsqrt_RL2 = mysqrt(R_RL2); %%%
Skk_RL2 = ComputeSkk(xkk1_RL2,Skk1_RL2,Rsqrt_RL2); %%%
predictedEntropy2(count) = det(Lambda*(Skk_RL2*Skk_RL2'));
reward_rel2 = abs(log(abs(preEntropy2 - predictedEntropy2(count))));
% reward_abs = 1/abs(log(predicted Entropy(count)));
predictedReward2(i) = reward_rel2*sign(preEntropy2 - predictedEntropy2(count));
% learing from prediction
agent2 = agent2.dpLearning(1,1,i,predictedReward2(i)); % there is only one state (1)
end
%%%%% Learning %%%%%
% trigering epsilon-greedy action
idx = agent2.egAction(1); % index of eps-greedy action
if idx == 0 % no learning yet
idx = fix(rand*length(para) + 1); % random selection
end
lmd = para(1,idx);
b = para(2,idx);
wf_lmd(expt, k) = lmd;
wf_b(expt, k) = b;
wf_idx(expt,k) = idx;
% computing R as the result of the applied action
R_RL2 = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1_RL2(1)-H); %%%
Rsqrt_RL2 = mysqrt(R_RL2); %%%
end
z_RL2 = z_idl + Rsqrt_RL2*mmm; %%%
[xkk_RL2,Skk_RL2] = Update(xkk1_RL2,Skk1_RL2,z_RL2,Rsqrt_RL2); %%%
% computing the new entropic state
newEntropy2 = det(Lambda*(Skk_RL2*Skk_RL2'));
% computing the reward
reward_rel2 = abs(log(abs(preEntropy2 - newEntropy2)));
reward_abs2 = 1/abs(log(newEntropy2));
reward2(k) = reward_rel2*sign(preEntropy2 - newEntropy2);
% reward(i)
% learning by Q-learning method
agent2 = agent2.dpLearning(1,1,idx,reward2(k)); % there is only one state (1)
% updating the previous entropy
preEntropy2 = newEntropy2;
time_new2(expt,k) = toc;
entropyBank2(expt,k) = preEntropy2;
%%%================================================================
%% RL3:
predictedEntropy3 = zeros(1,length(para)); % init. vector to speed up
predictedReward3 = zeros(1,length(para)); % init. vector to speed up
reward3 = zeros(1,N);
prePureReward = 0;
tic
if (k==1) || (k<30) || (rem(k,1/(fs_ctr*T))==0),
%%%%% Planning %%%%%
% tester = randWindowGenerator(numPlanningTrials, agent3.egAction(1), window, length(para));
for count = 1 : length(tester)%length(para),
i = tester(count);
theta = para(:,i)'; % fetch grid point (lmd, b)
lmd = theta(1);
b = theta(2);
%%% Calculate measurement covariance: R
R_RL3 = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1_RL3(1)-H); %%%
Rsqrt_RL3 = mysqrt(R_RL3); %%%
Skk_RL3 = ComputeSkk(xkk1_RL3,Skk1_RL3,Rsqrt_RL3); %%%
predictedEntropy3(count) = det(Lambda*(Skk_RL3*Skk_RL3'));
% reward_rel3 = abs(log(abs(preEntropy3 - predictedEntropy3(count))));
% predictedReward3(i) = reward_rel3*sign(preEntropy3 - predictedEntropy3(count)) + gamma_back*prePureReward;
% prePureReward = reward_rel3*sign(preEntropy3 - predictedEntropy3(count));
reward_rel3 = abs(log(abs(preEntropy3 - predictedEntropy3(count))));
% reward_abs = 1/abs(log(predicted Entropy(count)));
predictedReward3(i) = reward_rel3*sign(preEntropy3 - predictedEntropy3(count));
% learing from prediction
agent3 = agent3.dpLearning(1,1,i,predictedReward3(i)); % there is only one state (1)
end
%%%%% Learning %%%%%
% trigering epsilon-greedy action
idx = agent3.egAction(1); % index of eps-greedy action
if idx == 0 % no learning yet
idx = fix(rand*length(para) + 1); % random selection
elseif (k ~= 1)
if (abs(idx - preIdx) > window)
idx = preIdx;
countIdx = countIdx + 1;
%disp('<<<<< BREAK >>>>>');
end
end
lmd = para(1,idx);
b = para(2,idx);
wf_lmd(expt, k) = lmd;
wf_b(expt, k) = b;
wf_idx(expt,k) = idx;
% computing R as the result of the applied action
R_RL3 = computeR_FI(c, fc, lmd, b, r_snr0, M, xkk1_RL3(1)-H); %%%
Rsqrt_RL3 = mysqrt(R_RL3); %%%
end
z_RL3 = z_idl + Rsqrt_RL3*mmm; %%%
[xkk_RL3,Skk_RL3] = Update(xkk1_RL3,Skk1_RL3,z_RL3,Rsqrt_RL3); %%%
% computing the new entropic state
newEntropy3 = det(Lambda*(Skk_RL3*Skk_RL3'));
% computing the reward
reward_rel3 = abs(log(abs(preEntropy3 - newEntropy3)));
reward_abs3 = 1/abs(log(newEntropy3));
reward3(k) = reward_rel3*sign(preEntropy3 - newEntropy3);
% reward(i)
% learning by Q-learning method
agent3 = agent3.dpLearning(1,1,idx,reward3(k)); % there is only one state (1)
% updating the previous entropy
preEntropy3 = newEntropy3;
time_new3(expt,k) = toc;
entropyBank3(expt,k) = preEntropy3;
preIdx = idx; % the currently selected action
%%%================================================================
end % time
countIdx
percentage(expt) = countIdx/N; % average of non-switching in each MC run
end % MC run
Percentage = mean(percentage); % average of non-switching over MC
% timewdw = [1:N-2];
% %%======== Calculate mean =========================================
% xArray = mean(xArray_temp,3);
% xestArray = mean(xestArray_temp,3);
% xestArray_f = mean(xestArray_temp_f,3);
% xestArray_RL = mean(xestArray_temp_RL,3);
%
% % MSE = MSE/nExpt;
% % RMSE = MSE.^(0.5);
% % MSE_f = MSE_f/nExpt;
% % RMSE_f = MSE_f.^(0.5);
%
% d_ratio = 0.25;
%
% RMSE1 = reshape(mean(MSE),3,N).^(0.5);
% errbar1 = d_ratio*reshape(std(MSE),3,N).^(0.5);
%
% RMSE_f1 = reshape(mean(MSE_f),3,N).^(0.5);
% errbar1_f = d_ratio*reshape(std(MSE_f),3,N).^(0.5);
%
% RMSE_RL1 = reshape(mean(MSE_RL),3,N).^(0.5);
% errbar1_RL = d_ratio*reshape(std(MSE_RL),3,N).^(0.5);
%
% % ARMSE1 = mean(RMSE1');
% % ARMSE_f1 = mean(RMSE_f1');
%
% ARMSE1 = mean(mean(MSE,3),1).^0.5;
% ARMSE_f1 = mean(mean(MSE_f,3),1).^0.5;
% ARMSE_RL1 = mean(mean(MSE_RL,3),1).^0.5;
%%%=================================================================
%%%%%%%%%%%%%%%%%%RMSE plots%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% meanEntropy = mean(entropyBank);
% semilogy(1:N,meanEntropy,'k-d','linewidth',1)
% hold on
meanEntropy2 = mean(entropyBank2);
semilogy(1:N,meanEntropy2,'g-*','linewidth',1)
hold on
meanEntropy3 = mean(entropyBank3);
semilogy(1:N,meanEntropy3,'b-o','linewidth',1)
meanEntropyf = mean(entropyBankf);
semilogy(1:N,meanEntropyf,'r-d','linewidth',1)
xlabel('Perception-action cycles');
ylabel('Entropic-state');
hold off
h1 = gcf;
hfixed=findobj(h1,'LineStyle','-','Marker','d');
hgreen=findobj(h1,'LineStyle','-','Marker','*');
hblue=findobj(h1,'LineStyle','-','Marker','o');
legend([hfixed, hgreen, hblue],'Fixed waveform','No neighbourhood', 'Neighbourhood of 10');