def define_ha(settings, args):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
usafe_r = args[0]
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3", "x4"]
dim = len(ha.variables)
loc1 = ha.new_mode('loc1')
loc1.c_vector = np.array([0, 0, 0, 0], dtype=float)
print(loc1.c_vector.shape)
a_matrix = np.array(
[[1, 0, 0.1, 0], [0, 1, 0, 0.1], [0, 0, 0.8870, 0.0089], [0, 0, 0.0089, 0.8870]], dtype=float)
b_matrix = np.array([[0, 0], [0, 0], [1, 0], [0, 1]], dtype=float)
# Q = 1 * np.eye(dim)
Q = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 100]], dtype=float)
u_dim = len(b_matrix[0])
R = np.eye(u_dim)
(X, L, G) = care(a_matrix, b_matrix, Q, R)
control_f = open("./control_vals.txt", "a")
control_f.write("Q: " + str(Q) + "\n")
control_f.write("P: " + str(X) + "\n")
control_f.write("K: " + str(G) + "\n")
control_f.write("PBK: " + str(np.matmul(X, np.matmul(b_matrix, G))) + "\n")
control_f.write("PA: " + str(np.matmul(X, a_matrix)) + "\n")
control_f.write("A'P: " + str(np.matmul(a_matrix.T, X)) + "\n")
control_f.close()
k_matrix = np.array(G)
loc1.a_matrix = a_matrix - np.matmul(b_matrix, k_matrix)
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(loc1, error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0, 0.0, 0.0], 2.0))
usafe_set_constraint_list.append(LinearConstraint([1.0, 0.0, 0.0, 0.0], -1.0))
usafe_set_constraint_list.append(LinearConstraint([0.0, -1.0, 0.0, 0.0], 3))
usafe_set_constraint_list.append(LinearConstraint([0.0, 1.0, 0.0, 0.0], -2))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x", "y"]
loc1 = ha.new_mode('loc1')
loc1.a_matrix = np.array([[-0.1, 1], [-1, -0.1]])
# loc1.a_matrix = np.array([[0, 1], [-1, 0]])
loc1.c_vector = np.array([2, 0], dtype=float)
# loc1.set_dynamics(a_matrix, c_vector)
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(loc1, error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0], 2))
usafe_set_constraint_list.append(LinearConstraint([1.0, 0.0], 2))
usafe_set_constraint_list.append(LinearConstraint([0.0, -1.0], -1))
usafe_set_constraint_list.append(LinearConstraint([0.0, 1.0], 6))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def init_hr_to_star(settings, hr, mode):
'convert a HyperRectangle to a Star'
assert isinstance(mode, LinearAutomatonMode)
num_dims = len(hr.dims)
constraint_list = []
for i in range(num_dims):
(low, high) = hr.dims[i]
vector = np.array([1 if d == i else 0 for d in range(num_dims)],
dtype=float)
value = high
constraint_list.append(LinearConstraint(vector, value))
vector = np.array([-1 if d == i else 0 for d in range(num_dims)],
dtype=float)
value = -low
constraint_list.append(LinearConstraint(vector, value))
parent = InitParent(mode)
basis_matrix = np.identity(num_dims, dtype=float)
center = np.array([0.0] * num_dims, dtype=float)
return Star(settings, center, basis_matrix, constraint_list, parent, mode)
def compute_ce_vector(self,
simulation,
usafe_set_constraint_list,
direction=None,
sim_start_time=0,
current_mode_idx=0):
usafe_points = []
ce_vector = []
for time in self.error_time_steps[current_mode_idx]:
point = simulation[int(time) - sim_start_time]
usafe_lpi = LpInstance(self.num_dims, self.num_dims)
identity_matrix = np.identity(self.num_dims)
usafe_lpi.update_basis_matrix(np.identity(self.num_dims))
for dim in range(identity_matrix.ndim):
lc = LinearConstraint(identity_matrix[dim], point[dim])
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
lc = LinearConstraint(-1 * identity_matrix[dim], -point[dim])
usafe_lpi.add_basis_constraint(lc.vector, lc.value)
for constraints in usafe_set_constraint_list:
usafe_lpi.add_basis_constraint(constraints.vector,
constraints.value)
direction = np.zeros(self.num_dims)
usafe_point = np.zeros(self.num_dims)
is_feasible = usafe_lpi.minimize(direction,
usafe_point,
error_if_infeasible=False)
usafe_points.append(usafe_point)
if is_feasible:
ce_vector.append(1)
else:
ce_vector.append(0)
return ce_vector
def define_ha(settings, args):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
usafe_r = args[0]
x_ref = args[1]
step_inputs = args[2]
k_matrix = args[3]
a_matrices = args[4]
b_matrices = args[5]
dim = len(b_matrices[0])
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3", "x4", "t"]
locations = []
n_locations = len(step_inputs)
for idx in range(n_locations):
loc_name = 'loc' + str(idx)
loc = ha.new_mode(loc_name)
a_matrix = a_matrices[idx]
b_matrix = b_matrices[idx]
b_k_matrix = np.matmul(b_matrix, k_matrix)
loc.a_matrix = a_matrix + b_k_matrix
c_vector = -np.matmul(b_k_matrix, x_ref[idx])
c_vector = c_vector + np.matmul(b_matrix, step_inputs[idx])
c_vector[dim - 1] = step_size
# print(c_vector)
loc.c_vector = c_vector
loc.inv_list.append(
LinearConstraint([0.0, 0.0, 0.0, 0.0, 1.0],
step_size * idx)) # t <= 0.1
locations.append(loc)
for idx in range(n_locations - 1):
trans = ha.new_transition(locations[idx], locations[idx + 1])
trans.condition_list.append(
LinearConstraint([-0.0, -0.0, 0.0, 0.0, -1.0],
-step_size * idx)) # t >= 0.1
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(
LinearConstraint([1.0, 0.0, 0.0, 0.0, 0.0], -3.5))
# usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0, 0.0, 0.0, 0.0], -3.5))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for idx in range(n_locations - 1):
trans = ha.new_transition(locations[idx], error)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def test_eat_star_bs1_1d(self):
'test 1d eat-star with example-1 derived from the ball_string system'
settings = HylaaSettings(0.01, 2.0)
array = np.array
ha = LinearHybridAutomaton('Test Automaton')
ha.variables = ["x"]
mode = ha.new_mode('test_mode')
center = array([0.])
# x = 0.5 * alpha (2x = alpha)
# 0 <= alpha <= 1.0 -> (0 <= x <= 0.5)
cur_star = Star(settings, center, array([[0.5]]), [ \
LinearConstraint(array([1.]), 1.0), \
LinearConstraint(array([-1.]), 0.0)], \
None, mode)
# 2.0 <= alpha <= 3.0 -> (1.0 <= x <= 1.5)
new_star = Star(settings, center, array([[0.5]]), [ \
LinearConstraint(array([1.]), 3.0), \
LinearConstraint(array([-1.]), -2.0)], \
None, mode)
cur_star.eat_star(new_star)
# should be 0.0 <= alpha <= 3.0
self.assertAlmostEqual(cur_star.constraint_list[0].value, 3.0)
self.assertAlmostEqual(cur_star.constraint_list[1].value, 0.0)
def test_eat_star_bs2_1d(self):
'test 1d eat-star derived from example-2 of the ball_string system'
array = np.array
settings = HylaaSettings(0.01, 2.0)
ha = LinearHybridAutomaton('Test Automaton')
ha.variables = ["x"]
mode = ha.new_mode('test_mode')
center = array([0.])
basis_matrix = array([[1.0]], dtype=float)
# -alpha <= 1.0 ----> -1.0 <= alpha
# 2 * alpha <= -1 ----> alpha <= -0.5
cur_star = Star(settings, center, basis_matrix, [\
LinearConstraint(array([-1.]), 1.0), \
LinearConstraint(array([2.0]), -1.0),\
], \
None, mode)
# -0.7 <= alpha <= -0.6
new_star = Star(settings, center, basis_matrix, [\
LinearConstraint(array([-1.]), 0.7), \
LinearConstraint(array([1.]), -0.6), \
], \
None, mode)
cur_star.eat_star(new_star)
# should be unchanged: -0.0 <= alpha and 2 * alpha <= 1.0
self.assertAlmostEqual(cur_star.constraint_list[0].value, 1.0)
self.assertAlmostEqual(cur_star.constraint_list[1].value, -1.0)
def trim_to_invariant(self):
'''
trim the star to the mode's invariant.
returns (is_still_feasible, inv_vio_star_list)
'''
still_feasible = True
inv_vio_star_list = []
if len(self.mode.inv_list) > 0:
assert self.mode.num_inputs == 0, "mode invariants + dynamics with time-varying inputs not yet supported"
# check each invariant condition to see if it is violated
lpi = self.get_lpi()
for lin_con in self.mode.inv_list:
objective = np.array([-ele for ele in lin_con.vector], dtype=float)
result = np.zeros(2 * self.num_dims)
lpi.minimize(objective, result, error_if_infeasible=True)
offset = result[0:self.num_dims]
point = self.center + offset
val = np.dot(point, lin_con.vector)
if val > lin_con.value:
# add the constraint to the star's constraints
# first, convert the condition to the star's basis
# basis vectors (non-transpose) * standard_condition
basis_condition = np.dot(self.basis_matrix, lin_con.vector)
center_value = np.dot(self.center, lin_con.vector)
remaining_value = lin_con.value - center_value
basis_lc = LinearConstraint(basis_condition, remaining_value)
if self.settings.plot.plot_mode != PlotSettings.PLOT_NONE:
# use the inverse of the invariant constraint for plotting
inv_lc = LinearConstraint([-1 * ele for ele in basis_lc.vector], -basis_lc.value)
inv_vio_star = self.clone()
inv_vio_star.add_basis_constraint(inv_lc)
# re-check for feasibility after adding the constraint
if inv_vio_star.is_feasible():
inv_vio_star_list.append(inv_vio_star)
# add the constraint AFTER making the plot violation star
self.add_basis_constraint(basis_lc)
# we added a new constraint to the star, check if it's still feasible
if not self.is_feasible():
still_feasible = False
break # don't check the remaining invariant linear conditions
return (still_feasible, inv_vio_star_list)
def define_ha(settings, args):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
usafe_r = args[0]
if len(args) > 2:
x_ref = args[1]
step_inputs = args[2]
ha = LinearHybridAutomaton()
ha.variables = ["x", "y", "t"]
a_matrix = np.array([[2, -1, 0], [1, 0, 0], [0, 0, 1]])
b_matrix = np.array([[2], [0], [0]], dtype=float)
k_matrix = np.array([[-0.85559968, 0.46109066, 0]], dtype=float)
locations = []
n_locations = len(step_inputs)
for idx in range(n_locations):
loc_name = 'loc' + str(idx)
loc = ha.new_mode(loc_name)
b_k_matrix = np.matmul(b_matrix, k_matrix)
loc.a_matrix = a_matrix + b_k_matrix
c_vector = -np.matmul(b_k_matrix, x_ref[idx])
c_vector = c_vector + np.matmul(b_matrix, step_inputs[idx])
c_vector[len(ha.variables) - 1] = step_size
# print(c_vector)
loc.c_vector = c_vector
# loc.c_vector = np.array([step_inputs[idx], step_inputs[idx], 1], dtype=float)
loc.inv_list.append(LinearConstraint([0.0, 0.0, 1.0],
step_size * idx)) # t <= 0.1
locations.append(loc)
for idx in range(n_locations - 1):
trans = ha.new_transition(locations[idx], locations[idx + 1])
trans.condition_list.append(
LinearConstraint([-0.0, -0.0, -1.0], -step_size * idx)) # t >= 0.1
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(locations[0], error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0, 0.0], 1))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x", "y"]
loc1 = ha.new_mode('loc1')
a_matrix = np.array([[0.98965, 1.4747e-08], [7.4506e-09, 0]], dtype=float)
loc1.c_vector = np.array([0, 0], dtype=float)
b_matrix = np.array([[16], [0]], dtype=float)
Q = np.array([[1, 0], [0, 1]], dtype=float)
u_dim = len(b_matrix[0])
R = np.eye(u_dim)
(X, L, G) = care(a_matrix, b_matrix, Q, R)
control_f = open("./control_vals.txt", "a")
control_f.write("Q: "+str(Q)+"\n")
control_f.write("P: "+str(X)+"\n")
control_f.write("K: "+str(G)+"\n")
control_f.write("PBK: "+str(np.matmul(X, np.matmul(b_matrix, G)))+"\n")
control_f.write("PA: "+str(np.matmul(X, a_matrix))+"\n")
control_f.write("A'P: "+str(np.matmul(a_matrix.T, X))+"\n")
control_f.close()
k_matrix = np.array(G)
a_bk_matrix = a_matrix - np.matmul(b_matrix, k_matrix)
loc1.a_matrix = a_bk_matrix
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(loc1, error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0], -0.2))
usafe_set_constraint_list.append(LinearConstraint([0.0, 1.0], 0.0))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x", "y", "t"]
step_inputs = [[-0.6835318568657612], [-0.4274739688077575],
[0.4047028719575525], [-1.7181706660550653],
[0.6195838154872904], [-0.981255069072019],
[1.0521099187388827], [1.1240072822724865], [2.0],
[1.0260517738498387]]
a_matrix = np.array([[0, 2, 0], [1, 0, 0], [0, 0, 1]])
b_matrix = np.array([[1], [1], [0]], dtype=float)
locations = []
n_locations = len(step_inputs)
for idx in range(n_locations):
loc_name = 'loc' + str(idx)
loc = ha.new_mode(loc_name)
loc.a_matrix = a_matrix
c_vector = np.matmul(b_matrix, step_inputs[idx])
c_vector[len(ha.variables) - 1] = step_size
print(c_vector)
loc.c_vector = c_vector
# loc.c_vector = np.array([step_inputs[idx], step_inputs[idx], 1], dtype=float)
loc.inv_list.append(LinearConstraint([0.0, 0.0, 1.0], step_size * idx))
locations.append(loc)
for idx in range(n_locations - 1):
trans = ha.new_transition(locations[idx], locations[idx + 1])
trans.condition_list.append(
LinearConstraint([-0.0, -0.0, -1.0], -idx * step_size))
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(locations[0], error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0, 0.0], 1))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_init_states(ha):
'''returns a list of (mode, list(LinearConstraint])'''
# Variable ordering: [x, y]
rv = []
constraints = []
constraints.append(LinearConstraint([-1, 0], 5)) # -5.0 <= x
constraints.append(LinearConstraint([1, 0], -5)) # x <= -5.0
constraints.append(LinearConstraint([0, -1], 0)) # 0.0 <= y
constraints.append(LinearConstraint([0, 1], 0)) # y <= 0.0
rv.append((ha.modes['loc1'], constraints))
return rv
def define_ha(settings, usafe_r=None):
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["temp", "t"]
power = 7.0
high = 22.0
low = 18.0
c = 0.4
Tenv = 10.0
on = ha.new_mode('on')
on.a_matrix = np.array([[-c, 0.0], [0.0, 0.0]], dtype=float)
on.c_vector = np.array([Tenv * c + power, 1.0], dtype=float)
on.inv_list.append(LinearConstraint([1.0, 0.0], high)) # temp <= high
off = ha.new_mode('off')
off.a_matrix = np.array([[-c, 0.0], [0.0, 0.0]], dtype=float)
off.c_vector = np.array([Tenv * c, 1.0], dtype=float)
off.inv_list.append(LinearConstraint([-1.0, 0.0], -low)) # temp >= low
trans1_2 = ha.new_transition(on, off)
trans1_2.condition_list.append(LinearConstraint([-1.0, 0.0],
-high)) # temp > high
trans2_1 = ha.new_transition(off, on)
trans2_1.condition_list.append(LinearConstraint([1.0, 0.0],
low)) # temp < low
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0],
-21)) # temp >= high
# usafe_set_constraint_list.append(LinearConstraint([1.0, 0.0], low)) # temp <= low
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
trans1_error = ha.new_transition(on, error)
trans2_error = ha.new_transition(off, error)
for constraint in usafe_set_constraint_list:
trans1_error.condition_list.append(constraint)
trans2_error.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def test_eat_star_bs1_2d(self):
'test 2d eat-star derived from example-1 of the ball_string system'
array = np.array
mode = make_debug_mode()
center = array([0., 0.])
basis_matrix = array([[1.0, 0], [0, 0.5]])
cur_star = Star(HylaaSettings(0.01, 2.0), center, basis_matrix, [ \
LinearConstraint(array([1, 0]), 1), \
LinearConstraint(array([-1., 0.]), 0), \
LinearConstraint(array([0., 1.]), 1.0), \
LinearConstraint(array([0., -1.]), 0.0)], \
None, mode)
new_star = Star(HylaaSettings(0.01, 2.0), center, basis_matrix, [ \
LinearConstraint(array([1, 0]), 1), \
LinearConstraint(array([-1, 0]), 0), \
LinearConstraint(array([0., 1.]), 3.0), \
LinearConstraint(array([0., -1.]), -2.0)], \
None, mode)
cur_star.eat_star(new_star)
new_point = new_star.get_feasible_point()
self.assertTrue(cur_star.contains_point(new_point))
def test_eat_star_bs2_2d(self):
'test 2d eat-star derived from example-2 of the ball_string system'
array = np.array
mode = make_debug_mode()
settings = HylaaSettings(0.01, 2.0)
center = array([0., 0.])
basis_matrix = array([[1.0, 0], [0, 1.0]], dtype=float)
cur_star = Star(settings, center, basis_matrix, [\
LinearConstraint(array([-1., 0.]), 1.0), \
LinearConstraint(array([0., 1.]), 2.1), \
LinearConstraint(array([0., -1.]), -2.0), \
LinearConstraint(array([2.0, 0.]), -1),\
], \
None, mode)
new_star = Star(settings, center, basis_matrix, [\
LinearConstraint(array([-1., 0.]), 0.7), \
LinearConstraint(array([1., 0.]), -0.6), \
LinearConstraint(array([0., 1.]), 2.3), \
LinearConstraint(array([0., -1.]), -2.2), \
], \
None, mode)
cur_star.eat_star(new_star)
new_point = new_star.get_feasible_point()
self.assertTrue(cur_star.contains_point(new_point))
def add_std_constraint_direction(self, standard_direction):
'''
add a constraint direction, given in the standard basis to the star
'''
assert isinstance(standard_direction, np.ndarray)
assert standard_direction.shape == (self.num_dims, )
lpi = self.get_lpi()
basis_direction = np.dot(self.basis_matrix, standard_direction)
result = np.zeros((2 * self.num_dims))
# multiplying by -1 turns it into a maximization
lpi.minimize(-1 * standard_direction, result, error_if_infeasible=True)
opt_pt = result[:self.num_dims]
basis_pt = self.vector_to_star_basis(opt_pt)
opt_val = np.dot(basis_pt, basis_direction)
# offset the multiple to account for the stars' centers
opt_val -= np.dot(basis_direction, self.center)
lc = LinearConstraint(basis_direction, opt_val)
self.add_basis_constraint(lc)
def define_ha(settings, usafe_r=None):
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3", "x4"]
#
loc1 = ha.new_mode('loc1')
a_matrix = np.array([[1, 0, 0.1, 0], [0, 1, 0, 0.1],
[0, 0, 0.8870, 0.0089], [0, 0, 0.0089, 0.8870]],
dtype=float)
# exp 1
b_matrix = np.array([[1, 0], [0, 0], [1, 0], [0, 1]], dtype=float)
print(a_matrix, b_matrix)
R_mult_factor = 0.1
Q_matrix = np.eye(len(a_matrix[0]), dtype=float)
u_dim = len(b_matrix[0])
R_matrix = R_mult_factor * np.eye(u_dim)
print(a_matrix, b_matrix, Q_matrix, R_matrix)
k_matrix = get_input(a_matrix, b_matrix, Q_matrix, R_matrix)
print(k_matrix)
a_bk_matrix = a_matrix - np.matmul(b_matrix, k_matrix)
loc1.a_matrix = a_bk_matrix
loc1.c_vector = np.array([0.0, 0.0, 0.0, 0.0], dtype=float)
# print(a_bk_matrix)
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
# exp 1
# significant diff (10 sec) across equivalent/non-equ runs for p_intersect without reverse
# usafe_set_constraint_list.append(LinearConstraint([1.0, 0.0, 0.0, 0.0], -4.8))
# exp 2
# significant diff (13-15 sec) across equivalent/non-equ runs for p_intersect without reverse
# usafe_set_constraint_list.append(LinearConstraint([0.0, 0.0, 1.0, 0.0], -5.0))
# exp 3
usafe_set_constraint_list.append(
LinearConstraint([1.0, 0.0, 0.0, 0.0], -5.2))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
trans = ha.new_transition(loc1, error)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton(name="Oscillating Particle")
ha.variables = ["x", "y", "z"]
loc1 = ha.new_mode('loc1')
loc1.a_matrix = np.array([[0.722468865032875, -0.523371053120237, 0], [0.785056579680355, 0.696300312376864, 0], [0, 0, 0.930530895811206]])
loc1.c_vector = np.array([0, 0.1, 0.03], dtype=float)
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(loc1, error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([0, -1, 0], -0.5))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton(name="Damped Oscillator")
ha.variables = ["x", "y"]
loc1 = ha.new_mode('loc1')
loc1.a_matrix = np.array([[0.960659959352277, 0.194735414472060],
[-0.194735414472060, 0.960659959352277]])
loc1.c_vector = np.array([0.196702394590923, -0.019669801188631],
dtype=float)
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(loc1, error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([0.0, -1.0], -4))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def convert_usafe_basis_pred_in_basis_center(usafe_basis_pred,
basis_center):
offset = np.dot(usafe_basis_pred.vector, basis_center)
new_val = usafe_basis_pred.value - offset
new_lc = LinearConstraint(usafe_basis_pred.vector, new_val)
return new_lc
def define_ha(settings, usafe_r=None):
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3"]
#
loc1 = ha.new_mode('loc1')
loc1.a_matrix = np.array([[-0.1, -1, 0], [1, -0.1, 0], [0, 0, -0.15]])
loc1.c_vector = np.array([0, 0, 0], dtype=float)
# print(a_bk_matrix)
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
# exp 1
usafe_set_constraint_list.append(LinearConstraint([1, 0, 0], -0.46))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
trans = ha.new_transition(loc1, error)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha():
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "t"]
# input variable order: [u1, u2]
Model = ha.new_mode('Model')
a_matrix = np.array([[0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -1.0865, 8487.2, 0, 0, 0, 0, 0, 0], [-2592.1, -21.119, -698.91, -141399, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, -1.0865, 8487.2, 0, 0], [0, 0, 0, 0, -2592.1, -21.119, -698.91, -141399, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=float)
c_vector = np.array([0, 0, 0, 0, 0, 0, 0, 0, 1], dtype=float)
Model.set_dynamics(a_matrix, c_vector)
# u1 >= 0.16
# u1 <= 0.3
# u2 >= 0.2
# u2 <= 0.4
u_constraints_a = np.array([[-1, -0], [1, 0], [-0, -1], [0, 1]], dtype=float)
u_constraints_b = np.array([-0.16, 0.3, -0.2, 0.4], dtype=float)
b_matrix = np.array([[0, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, -1], [0, 0]], dtype=float)
Model.set_inputs(u_constraints_a, u_constraints_b, b_matrix)
_error = ha.new_mode('_error')
_error.is_error = True
trans = ha.new_transition(Model, _error)
trans.condition_list.append(LinearConstraint([0, 0, 0, 0, -1, 0, 0, 0, 0], -0.001501)) # 0.45 <= x5
return ha
def test_center_into_constraints_complex(self):
'''test that center_into_constraints doesn't modify the stars'''
mode = make_debug_mode()
array = np.array
star = Star(HylaaSettings(0.01, 2.0),
array([-0.11060623, -0.62105371]),
array([[-0.12748444, -6.33082449],
[0.06330825, -0.3807174]]),
[
LinearConstraint(array([1., 0.]), -0.95),
LinearConstraint(array([-1., 0.]), 1.05),
LinearConstraint(array([0., 1.]), 0.1),
LinearConstraint(array([0., -1.]), 0.1),
LinearConstraint(array([6.33082449, 0.3807174]),
-0.6210537093866693),
LinearConstraint(array([0.12748444, -0.06330825]),
-0.11060623185202963),
LinearConstraint(array([-0.12748444, 0.06330825]),
1.1106062318520296)
],
None,
mode,
extra_init=(None, 20, 0))
star2 = star.clone()
star2.center_into_constraints(star2.vector_to_star_basis(star2.center))
self.check_stars_equal(star, star2)
def test_init_constraints(self):
'test hylaa initialization using constraints'
hr = HyperRectangle([(-1, 4), (-1, 1)])
star = init_hr_to_star(make_settings(), hr, TestStar.loc)
# now try a list of LinearConstraints
constraints = [
LinearConstraint([-1, 0], 1),
LinearConstraint([1, 0], 4),
LinearConstraint([0, -1], 1),
LinearConstraint([0, 1], 1)
]
star2 = init_constraints_to_star(make_settings(), constraints,
TestStar.loc)
self.check_stars_equal(star, star2)
def compute_point_as_star_basis(self, point, error_star):
basis_predicates = []
identity_matrix = np.identity(self.num_dims, dtype=float)
for dim in range(identity_matrix.ndim):
lc = LinearConstraint(identity_matrix[dim], point[dim])
basis_predicates.append(LinearConstraint(lc.vector, lc.value))
lc = LinearConstraint(-1 * identity_matrix[dim], -point[dim])
basis_predicates.append(LinearConstraint(lc.vector, lc.value))
basis_predicates_in_star_basis = []
for lc in basis_predicates:
lc_vector = lc.vector
new_lc_vector = np.dot(error_star.basis_matrix, lc_vector)
new_lc_value = lc.value - np.dot(error_star.center, lc_vector)
basis_predicates_in_star_basis.append(LinearConstraint(new_lc_vector, new_lc_value))
return basis_predicates_in_star_basis
def define_ha(settings, usafe_r=None):
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2"]
#
loc1 = ha.new_mode('loc1')
# exp 1 and 2
a_matrix = np.array([[0.983498664120250, 0.101548195541291],
[-0.013528375561473, 0.935610369333783]],
dtype=float)
# exp 1
b_matrix = np.array([[0.0], [0.0]], dtype=float)
# # exp2
# b_matrix = np.array([[1], [1]], dtype=float)
print(a_matrix, b_matrix)
R_mult_factor = 0.2
Q_matrix = np.eye(len(a_matrix[0]), dtype=float)
u_dim = len(b_matrix[0])
R_matrix = R_mult_factor * np.eye(u_dim)
print(a_matrix, b_matrix, Q_matrix, R_matrix)
k_matrix = get_input(a_matrix, b_matrix, Q_matrix, R_matrix)
print(k_matrix)
# a_bk_matrix = a_matrix_ext - np.matmul(b_matrix_ext, k_matrix)
a_bk_matrix = a_matrix - np.matmul(b_matrix, k_matrix)
loc1.a_matrix = a_bk_matrix
loc1.c_vector = np.array([0.0, 0.0], dtype=float)
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
# exp 1
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0], -2.0))
# usafe_set_constraint_list.append(LinearConstraint([0.0, 1.0], -0.85))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
trans = ha.new_transition(loc1, error)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r=None):
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3", "x4"]
#
loc1 = ha.new_mode('loc1')
a_matrix = np.array(
[[1, 0, 0, 0], [0, 2, 0.5, 0], [0, 0, 1, 0], [0, 0, 0, 0.5]],
dtype=float)
# exp 1
b_matrix = np.array(
[[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 3, 0], [0, 2, 0, 1]], dtype=float)
print(a_matrix, b_matrix)
R_mult_factor = 0.1
Q_matrix = np.eye(len(a_matrix[0]), dtype=float)
u_dim = len(b_matrix[0])
R_matrix = R_mult_factor * np.eye(u_dim)
print(a_matrix, b_matrix, Q_matrix, R_matrix)
k_matrix = get_input(a_matrix, b_matrix, Q_matrix, R_matrix)
print(k_matrix)
a_bk_matrix = a_matrix - np.matmul(b_matrix, k_matrix)
loc1.a_matrix = a_bk_matrix
loc1.c_vector = np.array([0.0, 0.0, 0.0, 0.0], dtype=float)
# print(a_bk_matrix)
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
# exp 1
# usafe_set_constraint_list.append(LinearConstraint([0.0, 0.0, 0.0, 1.0], -2.9))
# exp 2
usafe_set_constraint_list.append(
LinearConstraint([0.0, 0.0, 0.0, 1.0], -3.42))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
trans = ha.new_transition(loc1, error)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def compute_usafe_std_pred_in_star_basis(self, error_star):
usafe_std_predicates = []
for usafe_set_lc in self.usafe_set_constraint_list:
## To correctly compute the dot product
lc_t = usafe_set_lc.vector
new_lc_value = usafe_set_lc.value - np.dot(error_star.center, lc_t)
usafe_std_predicates.append(LinearConstraint(usafe_set_lc.vector, new_lc_value))
return usafe_std_predicates
def define_ha(settings, usafe_r):
# x' = Ax + Bu + c
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8"]
loc1 = ha.new_mode('loc1')
a_matrix = np.array([[1, 0.1, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0.1, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0.1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0.1],
[0, 0, 0, 0, 0, 0, 0, 1]], dtype=float)
loc1.c_vector = np.array([0, 0, 0, 0, 0, 0, 0, 0], dtype=float)
b_matrix = np.array([[0, 0, 0, 0],
[0.1, 0, 0, 0],
[0, 0, 0, 0],
[0.1, -0.1, 0, 0],
[0, 0, 0, 0],
[0, 0.1, -0.1, 0],
[0, 0, 0, 0],
[0, 0, 0.1, -0.1]], dtype=float)
k_matrix = np.array([[401.0025, 40.0500, 1.0000, 0.0499, 0.0025, 0.0001, 0.0000, 0.0000],
[400.0025, 40.0001, -401.0000, -40.0499, 1.0000, 0.0499, 0.0025, 0.0001],
[400.0000, 40.0000, -400.0025, -40.0001, -401.0000, -40.0499, 1.0000, 0.0499],
[400.0000, 40.0000, -400.0000, -40.0000, -400.0025, -40.0001, -401.0025, -40.0500]], dtype=float)
loc1.a_matrix = a_matrix - np.matmul(b_matrix, k_matrix)
error = ha.new_mode('_error')
error.is_error = True
trans = ha.new_transition(loc1, error)
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([-1.0, 0.0, 0.0, 0.0], 2))
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
for constraint in usafe_set_constraint_list:
trans.condition_list.append(constraint)
return ha, usafe_set_constraint_list
def define_ha(settings, usafe_r=None):
'''make the hybrid automaton and return it'''
ha = LinearHybridAutomaton()
ha.variables = ["x", "v"]
extension = ha.new_mode('extension')
extension.a_matrix = np.array([[0.0, 1.0], [-100.0, -4.0]], dtype=float)
extension.c_vector = np.array([0.0, -9.81], dtype=float)
extension.inv_list.append(LinearConstraint([1.0, 0.0], 0)) # x <= 0
freefall = ha.new_mode('freefall')
freefall.a_matrix = np.array([[0.0, 1.0], [0.0, 0.0]], dtype=float)
freefall.c_vector = np.array([0.0, -9.81], dtype=float)
freefall.inv_list.append(LinearConstraint([-1.0, 0.0], 0.0)) # 0 <= x
freefall.inv_list.append(LinearConstraint([1.0, 0.0], 1.0)) # x <= 1
trans = ha.new_transition(extension, freefall)
trans.condition_list.append(LinearConstraint([-0.0, -1.0], -0.0)) # v >= 0
error = ha.new_mode('_error')
error.is_error = True
usafe_set_constraint_list = []
if usafe_r is None:
usafe_set_constraint_list.append(LinearConstraint([0.0, -1.0], -6.5))
# usafe_set_constraint_list.append(LinearConstraint([3.0, -1.0], -7)) # for line with pts (-1, 4) and (0, 7)
else:
usafe_star = init_hr_to_star(settings, usafe_r, ha.modes['_error'])
for constraint in usafe_star.constraint_list:
usafe_set_constraint_list.append(constraint)
trans1 = ha.new_transition(extension, error)
for constraint in usafe_set_constraint_list:
trans1.condition_list.append(constraint)
trans2 = ha.new_transition(freefall, error)
for constraint in usafe_set_constraint_list:
trans2.condition_list.append(constraint)
return ha, usafe_set_constraint_list
