Implementation of Integral Cost function in Matlab
12 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Please, I need ideas how to simulate the model in the attached document. writing code for equation 39 - 41 is trivial, however, I am not sure how to write the code for equation 42.
I implemented the code below for one time step and assuming that the control input u = 0.1. The question is it correct to compute the optimal cost function like this or there is a better way. Please, find attached the model.
tspan = [0,1];
x0 = 1;
u = 0.1;
tau = 1;
xn = 1;
[time, dxdt, J] = plant_dynamics(tspan,x0,u, tau, xn);
%% System Dynamics
function [time, dxdt, J] = plant_dynamics(tspan,x0,u, tau, xn)
[time, dxdt] = ode23(@solve_ode,tspan,x0);
J = xn + integral_cost(dxdt, u);
function dx = solve_ode(t,x)
A = 1 + tau/12000;
B = 1 + 0.25 * sin(2*pi*t/3000);
dx = A*x + B * u;
end
function int_J = integral_cost(dxdt, u)
x = dxdt;
integral_J = x.^2 + u.^2;
int_J = trapz(integral_J);
end
end
0 Kommentare
Akzeptierte Antwort
VBBV
am 18 Aug. 2022
Bearbeitet: VBBV
am 18 Aug. 2022
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
0 Kommentare
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Get Started with Optimization Toolbox finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!