def construct_unsafe_set(dae_auto):
'construct unsafe set'
# unsafe set: x_478 >= 0.05
C1 = dae_auto.matrix_c.todense()
C = -C1[0]
d = np.array([[-0.05]]) # safe
print "\nunsafe_set 1: matrix C = {}".format(C)
print "\nunsafe_set 1: vector d = {}".format(d)
unsafe_set1 = LinearPredicate(C, d)
d = np.array([[-0.01]]) # unsafe
print "\nunsafe_set 2: matrix C = {}".format(C)
print "\nunsafe_set 2: vector d = {}".format(d)
unsafe_set2 = LinearPredicate(C, d)
unsafe_set = [unsafe_set1, unsafe_set2] # list of unsafe set
return unsafe_set
def construct_unsafe_set(dae_auto):
'construct unsafe set'
C = np.array([[-1, 0, -1, 0, 0]]) # x(0) + x(2) >= 0.2
d = np.array([[-0.2]])
print "\nunsafe_set 1: matrix C = {}".format(C)
print "\nunsafe_set 1: vector d = {}".format(d)
unsafe_set1 = LinearPredicate(C, d)
C = np.array([[0, 0, 0, 1, 0]]) # x(3) <= -0.1
d = np.array([[-0.3]])
print "\nunsafe_set 2: matrix C = {}".format(C)
print "\nunsafe_set 2: vector d = {}".format(d)
unsafe_set2 = LinearPredicate(C, d)
unsafe_set = [unsafe_set1, unsafe_set2] # list of unsafe set
return unsafe_set
def verify_large_stokes_equation(N):
'verify a large stokes equation'
E, A, B, C = get_benchmark(1.0, N)
dae_sys = construct_dae_automaton(E, A, B, C)
dae_auto = convert_to_auto_dae(dae_sys)
decoupled_dae = decouple_auto_dae(dae_auto)
basic_matrix = generate_consistent_basic_matrix(decoupled_dae)
init_set = construct_init_set(basic_matrix)
totime = 0.4
num_steps = 100
solver_names = ['vode', 'zvode', 'lsoda', 'dopri5',
'dop853'] # similar to ode45 mathlab
# unsafe set: - vcx - vcy <=
c_mat = dae_auto.matrix_c.todense()
C1 = c_mat[0]
C2 = c_mat[1]
C = -C1 - C2
d = np.array([[0.04]]) # unsafe
print "\nunsafe_set 1: matrix C = {}".format(C)
print "\nunsafe_set 1: vector d = {}".format(d)
unsafe_set1 = LinearPredicate(C, d)
C = -C1
d = np.array([[-0.2]]) # safe vcx >= 0.2
print "\nunsafe_set 2: matrix C = {}".format(C)
print "\nunsafe_set 2: vector d = {}".format(d)
unsafe_set2 = LinearPredicate(C, d)
unsafe_set = [unsafe_set1, unsafe_set2] # list of unsafe set
# verify the safety of the system'
n = len(unsafe_set)
ver_res = []
for i in xrange(0, n):
us = unsafe_set[i]
vr = Verifier().check_safety(
dae_auto, init_set, us, totime, num_steps, solver_names[3],
'vr_dimension_{}_case_{}'.format(E.shape[0], i))
ver_res.append(vr)
return ver_res
def construct_unsafe_set(dae_auto):
'construct unsafe set'
# unsafe set: p_c >= 1.0 and v_c >= 1.5, the middle mass position
c_mat = dae_auto.matrix_c.todense()
C = -c_mat
d = np.array([[-1.0], [-1.5]])
print "\nunsafe_set 1: matrix C = {}".format(C)
print "\nunsafe_set 1: vector d = {}".format(d)
unsafe_set1 = LinearPredicate(C, d)
C = -c_mat[1] # v_c <= -0.2
d = np.array([[0.2]])
print "\nunsafe_set 2: matrix C = {}".format(C)
print "\nunsafe_set 2: vector d = {}".format(d)
unsafe_set2 = LinearPredicate(C, d)
unsafe_set = [unsafe_set1, unsafe_set2] # list of unsafe set
return unsafe_set
def construct_unsafe_set(dae_auto):
'construct unsafe set'
n = dae_auto.matrix_a.shape[0]
In = np.eye(n)
C = In[0:2, :] # first and second state variables
d = np.array([[-0.2], [-0.1]])
print "\nunsafe_set 1: matrix C = {}".format(C)
print "\nunsafe_set 1: vector d = {}".format(d)
unsafe_set1 = LinearPredicate(C, d)
C = -In[0:1, :] # first state variable
d = np.array([[-0.2]])
print "\nunsafe_set 2: matrix C = {}".format(C)
print "\nunsafe_set 2: vector d = {}".format(d)
unsafe_set2 = LinearPredicate(C, d)
unsafe_set = [unsafe_set1, unsafe_set2] # list of unsafe set
return unsafe_set
def construct_unsafe_set(dae_auto):
'construct unsafe set'
# unsafe set: x_1 >= 0.03
C1 = dae_auto.matrix_c.todense()
C = -C1[0]
d = np.array([[-0.03]]) # safe
# d = np.array([[-0.01]]) # unsafe
print "\nunsafe matrix C = {}".format(C)
print "\nunsafe vector d = {}".format(d)
unsafe_set = LinearPredicate(C, d)
return unsafe_set
def construct_unsafe_set1(dae_auto):
'construct unsafe set'
# unsafe set: - vcx - vcy <=
c_mat = dae_auto.matrix_c.todense()
C1 = c_mat[0]
C2 = c_mat[1]
C = -C1 - C2
d = np.array([[0.04]])
print "\nunsafe matrix C = {}".format(C)
print "\nunsafe vector d = {}".format(d)
unsafe_set = LinearPredicate(C, d)
return unsafe_set