H infinity filtering for linear system

Hi everybody!

I am trying to design an event-triggered H-infinity filter for a linear system, Can anybody provide any reference coding for this??

[Uzair Ahmed]

function hinfinity(g, duration, dt, SteadyState)

%

function hinfinity(g, duration, dt, SteadyState)

%

% H-infinity filter simulation for a vehicle travelling along a road.

% This code also simulates the Kalman filter.

% INPUTS

% g = gamma

% if g is too large the program will terminate with an error message.

% In my simulation I set g = 0.01.

% duration = length of simulation (seconds). I used duration = 60.

% dt = step size (seconds). I used dt = 0.1.

% SteadyState = flag indicating use of steady state filter.

% 1 = steady state, 0 = time-varying

measnoise = 2;

% nominal velocity measurement noise (feet/sec)

accelnoise = 0.2;

% nominal acceleration noise (feet/sec^2)

a = [1 dt; 0 1];

% transition matrix

b = [dt^2/2; dt];

% input matrix

c = [0 1];

% measurement matrix

x = [0; 0];

% initial state vector

y = c * x;

% initial measurement

% Initialize Kalman filter variables

xhat = x;

% initial Kalman filter state estimate

Sz = measnoise^2;

% measurement error covariance

Sw = accelnoise^2 * [dt^4/4 dt^3/2; dt^3/2 dt^2];

% process noise cov

P = Sw;

% initial Kalman filter estimation covariance

% Initialize H-infinity filter variables

xhatinf = x;

% initial H-infinity filter state estimate

Pinf = 0.01*eye(2);

W = [0.0003 0.0050; 0.0050 0.1000]/1000;

V = 0.01;

Q = [0.01 0; 0 0.01];

% Initialize arrays for later plotting.

pos = [x(1)];

% true position array

vel = [x(2)];

% true velocity array

poshat = [xhat(1)];

% estimated position array (Kalman filter)

velhat = [xhat(2)];

% estimated velocity array (Kalman filter)

poshatinf = [xhatinf(1)];

% estimated position array (H-infinity)

velhatinf = [xhatinf(2)];

% estimated velocity array (H-infinity)

HinfGains = [0; 0];

% H-infinity filter gains

KalmanGains = [0; 0];

% Kalman filter gains

for t = 0 : dt: duration-dt

% Use a constant commanded acceleration of 1 foot/sec^2.

u = 1;

% Figure out the H-infinity estimate.

if (SteadyState == 1)

% Use steady-state H-infinity gains

K = [0.11; 0.09];

else

L = inv(eye(2) - g * Q * Pinf + c' * inv(V) * c * Pinf);

K = a * Pinf * L * c' * inv(V);

Pinf = a * Pinf * L * a' + W;

% Force Pinf to be symmetric.

Pinf = (Pinf + Pinf') / 2;

% Make sure the eigenvalues of Pinf are less than 1 in magnitude.

lambda = eig(Pinf);

if (abs(lambda(1)) >= 1) | (abs(lambda(2)) >= 1)

disp('gamma is too large');

return;

end

end

xhatinf = a * xhatinf + b * u + K * (y - c * xhatinf);

HinfGains = [HinfGains K];

poshatinf = [poshatinf; xhatinf(1)];

velhatinf = [velhatinf; xhatinf(2)];

% Simulate the linear system and noisy measurement.

% Note that randn is Matlab's Gaussian (normal) random number

% generator; rand is Matlab's uniform random number generator.

ProcessNoise = 2 * accelnoise * b .* [randn; randn];

x = a * x + b * u + ProcessNoise;

MeasNoise = measnoise * (rand - 0.5);

y = c * x + MeasNoise;

% Compute the Kalman filter estimate.

% Extrapolate the most recent state estimate to the present time.

xhat = a * xhat + b * u;

poshat = [poshat; xhat(1)];

velhat = [velhat; xhat(2)];

% Form the Innovation vector.

Inn = y - c * xhat;

if (SteadyState == 1)

K = [0.1; 0.01];

else

% Compute the covariance of the Innovation.

s = c * P * c' + Sz;

% Form the Kalman Gain matrix.

K = a * P * c' * inv(s);

% Compute the covariance of the estimation error.

P = a * P * a' - a * P * c' * inv(s) * c * P * a' + Sw;

% Force P to be symmetric.

P = (P + P') / 2;

end

% Update the Kalman filter state estimate.

xhat = xhat + K * Inn;

% Save some parameters for plotting later.

KalmanGains = [KalmanGains K];

pos = [pos; x(1)];

vel = [vel; x(2)];

end

% Plot the results

close all;

% Close all open figures

t = 0 : dt : duration;

% Create a time array

% Plot the position estimation error

% (Kalman filter = red line, H-infinity filter = green line)

figure;

plot(t,pos-poshat,'r', t,pos-poshatinf,'g');

grid;

xlabel('Time (sec)');

ylabel('Position Error (feet)');

title('Position Estimation Error');

% Plot the velocity estimation error

% (Kalman filter = red line, H-infinity filter = green line)

figure;

plot(t,vel-velhat,'r', t,vel-velhatinf,'g');

grid;

xlabel('Time (sec)');

ylabel('Velocity Error (feet)');

title('Velocity Estimation Error');

% Plot the Kalman filter gain matrix

figure;

plot(t,KalmanGains(1,:),'r', t,KalmanGains(2,:),'g');

grid;

xlabel('Time (sec)');

title('Kalman Gains');

% Plot the H-infinity filter gain matrix

figure;

plot(t,HinfGains(1,:),'r', t,HinfGains(2,:),'g');

grid;

xlabel('Time (sec)');

title('H-Infinity Gains');