# Initialize symbolic variables
x1, x2, u = sp.symbols('x1,x2,u')
umax = 1
data = { # dynamics
'x_vars': [x1, x2],
'u_vars': [u],
'vector_field': [1, u],
# domains
'X': [(x1-(2))*(2-x1), (x2-(-2))*(2-x2)],
'U': [(u-(-umax))*(umax-u)],
# specification
'K': [(x1-(-0))*(1-x1), (x2-(-1))*(1-x2)],
# parameters
'maxdeg' : 10,
'tol': 1e-10,
'r': 0, # currently not used
'alpha': 0.05}
rho = compute_reach_not(data)
fig1 = plt.figure(1)
plot2d_invariance(rho, data, [(umax,), (-umax,)], fig1.gca())
fig2 = plt.figure(2)
plot2d_surf(rho, data, fig2.gca(projection='3d'))
plt.show()
tmax = 1
d1max = 0.25
d2max = 0.1
data = { # dynamics
'x_vars': [x1, x2],
'd_vars': [d1, d2],
'vector_field': [-(0.2+d1)*x1-x2, x1-0.2*x2+d2],
# domains
'X': [(x1-(-2))*(2-x1), (x2-(-2))*(2-x2)],
'D': [(d1-(-d1max))*(d1max-d1), (d2-(-d2max))*(d2max-d2)],
# specification
'K': [(x1-(-1.5))*(1.5-x1), (x2-(-1.5))*(1.5-x2)],
# parameters
'maxdeg' : 10,
'tol': 1e-10,
'r': 0, # currently not used
'alpha': 0.05}
rho = compute_inv_mosek_not(data)
fig1 = plt.figure(1)
plot2d_invariance(rho, data, list(product([-d1max, d1max], [-d2max, d2max])), fig1.gca())
fig2 = plt.figure(2)
plot2d_surf(rho, data, fig2.gca(projection='3d'))
plt.show()
