tspan = [0,1];
x0 = 1;
u = 0.1;
tau = 1;
xn = 1; % noise
[time, dxdt, J] = plant_dynamics(tspan,x0,u, tau, xn);
subplot(211)
plot(time,dxdt); title('Plant response')
subplot(212)
plot(time,J);title(' cost function (J) varying with noise input ')
%% System Dynamics
function [time, dxdt, J] = plant_dynamics(tspan,x0,u, tau, xn)
[time, dxdt] = ode23(@solve_ode,tspan,x0);
for k = 1:length(dxdt)
J(k,:) = (rand(1)*xn *dxdt).^2 + integral_cost(dxdt, u,xn); % add noise here
end
function dxdt = solve_ode(t,x)
A = 1 + tau/12000;
B = 1 + 0.25 * sin(2*pi*t/3000);
dxdt = A*x + B * u ;
end
function int_J = integral_cost(dxdt, u,xn)
x = dxdt;
integral_J = x.^2 + u.^2;
int_J = trapz(integral_J,xn);
end
end
