Exemplo n.º 1
0
def find_discrete_state(x0, part):
    """Return index identifying the discrete state
    to which the continuous state x0 belongs to.

    Notes
    =====
    1. If there are overlapping partitions
        (i.e., x0 belongs to more than one discrete state),
        then return the first discrete state ID

    @param x0: initial continuous state
    @type x0: numpy 1darray

    @param part: state space partition
    @type part: L{PropPreservingPartition}

    @return: if C{x0} belongs to some
        discrete state in C{part},
        then return the index of that state

        Otherwise return None, i.e., in case
        C{x0} does not belong to any discrete state.
    @rtype: int
    """
    for (i, region) in enumerate(part):
        if pc.is_inside(region, x0):
            return i
    return None
Exemplo n.º 2
0
def find_discrete_state(x0, part):
    """Return index identifying the discrete state
    to which the continuous state x0 belongs to.

    Notes
    =====
    1. If there are overlapping partitions
        (i.e., x0 belongs to more than one discrete state),
        then return the first discrete state ID

    @param x0: initial continuous state
    @type x0: numpy 1darray

    @param part: state space partition
    @type part: L{PropPreservingPartition}

    @return: if C{x0} belongs to some
        discrete state in C{part},
        then return the index of that state

        Otherwise return None, i.e., in case
        C{x0} does not belong to any discrete state.
    @rtype: int
    """
    for (i, region) in enumerate(part):
        if pc.is_inside(region, x0):
            return i
    return None
Exemplo n.º 3
0
 def is_inside_test(self):
     box = [[0.0, 1.0], [0.0, 2.0]]
     p = pc.Polytope.from_box(box)
     point = np.array([0.0, 1.0])
     abs_tol = 0.01
     assert pc.is_inside(p, point)
     assert pc.is_inside(p, point, abs_tol)
     region = pc.Region([p])
     assert pc.is_inside(region, point)
     assert pc.is_inside(region, point, abs_tol)
     point = np.array([2.0, 0.0])
     assert not pc.is_inside(p, point)
     assert not pc.is_inside(p, point, abs_tol)
     region = pc.Region([p])
     assert not pc.is_inside(region, point)
     assert not pc.is_inside(region, point, abs_tol)
     abs_tol = 1.2
     assert pc.is_inside(p, point, abs_tol)
     assert pc.is_inside(region, point, abs_tol)
Exemplo n.º 4
0
def is_seq_inside(x0, u_seq, ssys, P0, P1):
    """Checks if the plant remains inside P0 for time t = 1, ... N-1
    and  that the plant reaches P1 for time t = N.
    Used to test a computed input sequence.
    No disturbance is taken into account.

    @param x0: initial point for execution
    @param u_seq: (N x m) array where row k is input for t = k

    @param ssys: dynamics
    @type ssys: L{LtiSysDyn}

    @param P0: C{Polytope} where we want x(k) to remain for k = 1, ... N-1

    @return: C{True} if x(k) \in P0 for k = 1, .. N-1 and x(N) \in P1.
        C{False} otherwise
    """
    N = u_seq.shape[0]
    x = x0.reshape(x0.size, 1)

    A = ssys.A
    B = ssys.B
    if len(ssys.K) == 0:
        K = np.zeros(x.shape)
    else:
        K = ssys.K

    inside = True
    for i in range(N - 1):
        u = u_seq[i, :].reshape(u_seq[i, :].size, 1)
        x = A.dot(x) + B.dot(u) + K

        if not pc.is_inside(P0, x):
            inside = False

    un_1 = u_seq[N - 1, :].reshape(u_seq[N - 1, :].size, 1)
    xn = A.dot(x) + B.dot(un_1) + K

    if not pc.is_inside(P1, xn):
        inside = False

    return inside
Exemplo n.º 5
0
def is_seq_inside(x0, u_seq, ssys, P0, P1):
    """Checks if the plant remains inside P0 for time t = 1, ... N-1
    and  that the plant reaches P1 for time t = N.
    Used to test a computed input sequence.
    No disturbance is taken into account.

    @param x0: initial point for execution
    @param u_seq: (N x m) array where row k is input for t = k

    @param ssys: dynamics
    @type ssys: L{LtiSysDyn}

    @param P0: C{Polytope} where we want x(k) to remain for k = 1, ... N-1

    @return: C{True} if x(k) \in P0 for k = 1, .. N-1 and x(N) \in P1.
        C{False} otherwise
    """
    N = u_seq.shape[0]
    x = x0.reshape(x0.size, 1)

    A = ssys.A
    B = ssys.B
    if len(ssys.K) == 0:
        K = np.zeros(x.shape)
    else:
        K = ssys.K

    inside = True
    for i in range(N - 1):
        u = u_seq[i, :].reshape(u_seq[i, :].size, 1)
        x = A.dot(x) + B.dot(u) + K

        if not pc.is_inside(P0, x):
            inside = False

    un_1 = u_seq[N - 1, :].reshape(u_seq[N - 1, :].size, 1)
    xn = A.dot(x) + B.dot(un_1) + K

    if not pc.is_inside(P1, xn):
        inside = False

    return inside
Exemplo n.º 6
0
        print('Discrete time: k = ' +str(i) )
        print('\t u[' +str(i) +"]' = " +str(u.T) )
        print('\t x[' +str(i) +"]' = " +str(x.T) +'\n')

    print('completed continuous transition iteration')
    return x

x0 = np.array([0.5, 0.6])
start = find_discrete_state(x0, disc_dynamics.ppp)
end = 14

start_poly = disc_dynamics.ppp.regions[start]
end_poly = disc_dynamics.ppp.regions[end]

if not is_inside(start_poly, x0):
    raise Exception('x0 \\notin start_poly')

start_state = start
end_state = end

post = disc_dynamics.ts.states.post(start_state)
print(post)
if not end_state in post:
    raise Exception('end \\notin post(start)')

u_seq = get_input(x0, sys_dyn, disc_dynamics,
              start, end)
print('Computed input sequence: u = ')
print(u_seq)
Exemplo n.º 7
0
        print('Discrete time: k = ' + str(i))
        print('\t u[' + str(i) + "]' = " + str(u.T))
        print('\t x[' + str(i) + "]' = " + str(x.T) + '\n')

    print('completed continuous transition iteration')
    return x


x0 = np.array([0.5, 0.6])
start = find_discrete_state(x0, disc_dynamics.ppp)
end = 14

start_poly = disc_dynamics.ppp.regions[start]
end_poly = disc_dynamics.ppp.regions[end]

if not is_inside(start_poly, x0):
    raise Exception('x0 \\notin start_poly')

start_state = 's' + str(start)
end_state = 's' + str(end)

post = disc_dynamics.ts.states.post(start_state)
print(post)
if not end_state in post:
    raise Exception('end \\notin post(start)')

u_seq = get_input(x0, sys_dyn, disc_dynamics, start, end)
print('Computed input sequence: u = ')
print(u_seq)

x = integrate(sys_dyn, x0, u_seq)