from gekko import GEKKO
import numpy as np
m = GEKKO()
m.time = np.linspace(0,8,81)
t = m.Param(m.time)
u = m.MV(1,lb=0,ub=5); u.STATUS=1
x = m.Var(1)
m.periodic(u)
m.periodic(x)
m.Minimize((x-3)**2)
m.Equation(x.dt()+x==m.cos(t)+u)
m.options.IMODE = 6
m.solve()

import matplotlib.pyplot as plt
plt.plot(m.time,u,m.time,x)
plt.legend(['u','x'])
plt.show()