def dyns_1D(a):
x0 = reshape_pt1(a[:x.shape[1]])
u0 = reshape_pt1(a[x.shape[1]:])
version = \
lambda t, xl, ul, t0, init_control, process_noise_var, **kwargs: \
duffing_continuous_prior_mean(xl, ul, kwargs)
xnext = dynamics_traj(x0=x0,
u=u0,
t0=0,
dt=dt,
init_control=u0,
discrete=False,
version=version,
meas_noise_var=0,
process_noise_var=0,
method='RK45',
t_span=[0, dt],
t_eval=[dt],
kwargs=prior_kwargs)
return reshape_pt1_tonormal(xnext)
# Return xi_t instead of x_t+1 from x_t,u_t
true_dynamics = lambda x, control: \
- dyn_kwargs.get('beta') * x[:, 0] ** 3 - dyn_kwargs.get('alpha') \
* x[:, 0] - dyn_kwargs.get('delta') * x[:, 1]
elif ('justvelocity' in system) and ('Duffing' in system):
if not continuous_model:
true_dynamics = lambda x, control: dynamics_traj(
x0=reshape_pt1(x),
u=lambda t, kwarg, t0, init_control: interpolate(
t,
np.concatenate(
(reshape_dim1(np.arange(len(control))), control),
axis=1),
t0=t0,
init_value=init_control),
t0=t0,
dt=dt,
init_control=init_control,
version=dynamics,
meas_noise_var=0,
process_noise_var=process_noise_var,
method=optim_method,
t_span=[0, dt],
t_eval=[dt],
kwargs=dyn_kwargs)[:, -1]
else:
true_dynamics = lambda x, control: \
dynamics(t=t0, x=x, u=lambda t, kwarg, t0, init_control:
interpolate(t, np.concatenate((reshape_dim1(np.arange(
len(control))), control), axis=1), t0=t0,
init_value=init_control),
def simulate_dynamics(t_span,
t_eval,
t0,
dt,
init_control,
init_state,
dynamics,
controller,
process_noise_var,
optim_method,
dyn_config,
discrete=False,
verbose=False):
xtraj = dynamics_traj(x0=reshape_pt1(init_state),
u=controller,
t0=t0,
dt=dt,
init_control=init_control,
discrete=discrete,
version=dynamics,
meas_noise_var=0,
process_noise_var=process_noise_var,
method=optim_method,
t_span=t_span,
t_eval=t_eval,
kwargs=dyn_config)
utraj = controller(t_eval,
kwargs=dyn_config,
t0=t0,
init_control=init_control)
t_utraj = np.concatenate((reshape_dim1(t_eval), utraj), axis=1)
# Trajectory
plt.plot(t_eval, xtraj[:, 0], label='Position')
plt.plot(t_eval, xtraj[:, 1], label='Velocity')
plt.title('States over time')
plt.xlabel('t')
plt.ylabel('x')
plt.legend()
if verbose:
plt.show()
if xtraj.shape[1] > 2:
for i in range(2, xtraj.shape[1]):
plt.plot(t_eval, xtraj[:, i], label='True dim ' + str(i))
plt.title('Dim ' + str(i) + ' over time')
plt.xlabel('t')
plt.ylabel('x')
plt.legend()
if verbose:
plt.show()
# Phase portrait
plt.plot(xtraj[:, 0], xtraj[:, 1], label='Trajectory')
plt.title('Phase portrait')
plt.xlabel('x')
plt.ylabel(r'$\dot{x}$')
plt.legend()
if verbose:
plt.show()
plt.close('all')
plt.clf()
return xtraj, utraj, t_utraj