"""
Linear dynamical system
"""
import jax
import jax.numpy as np
import jax.random as random
import tigercontrol
from tigercontrol.utils import generate_key
from tigercontrol.problems.control import ControlProblem
[docs]class LDS_Control(ControlProblem):
"""
Description: Simulates a linear dynamical system.
"""
[docs] def __init__(self):
self.initialized = False
def initialize(self, n, m, d, noise=1.0):
"""
Description: Randomly initialize the hidden dynamics of the system.
Args:
n (int): Input dimension.
m (int): Observation/output dimension.
d (int): Hidden state dimension.
noise (float): Default value 1.0. The magnitude of the noise (Gaussian) added
to both the hidden state and the observable output.
Returns:
The first value in the time-series
"""
self.initialized = True
self.T = 0
self.n, self.m, self.d, self.noise = n, m, d, noise
# shrinks matrix M such that largest eigenvalue has magnitude k
normalize = lambda M, k: k * M / np.linalg.norm(M, ord=2)
# initialize matrix dynamics
self.A = random.normal(generate_key(), shape=(d, d))
self.B = random.normal(generate_key(), shape=(d, n))
self.C = random.normal(generate_key(), shape=(m, d))
self.D = random.normal(generate_key(), shape=(m, n))
self.h = random.normal(generate_key(), shape=(d,))
# adjust dynamics matrix A
self.A = normalize(self.A, 1.0)
self.B = normalize(self.B, 1.0)
self.C = normalize(self.C, 1.0)
self.D = normalize(self.D, 1.0)
def _step(u, h, eps):
eps_h, eps_y = eps
next_h = np.dot(self.A, h) + np.dot(self.B, u) + self.noise * eps_h
y = np.dot(self.C, next_h) + np.dot(self.D, u) + self.noise * eps_y
return (next_h, y)
self._step = jax.jit(_step)
y = np.dot(self.C, self.h) + np.dot(self.D, np.zeros(n)) + noise * random.normal(generate_key(), shape=(m,))
return y
def step(self, u):
"""
Description: Moves the system dynamics one time-step forward.
Args:
u (numpy.ndarray): control input, an n-dimensional real-valued vector.
Returns:
A new observation from the LDS.
"""
assert self.initialized
assert u.shape == (self.n,)
self.T += 1
self.h, y = self._step(u, self.h, (random.normal(generate_key(), shape=(self.d,)), random.normal(generate_key(), shape=(self.m,))))
return y
def hidden(self):
"""
Description: Return the hidden state of the system.
Args:
None
Returns:
h: The hidden state of the LDS.
"""
assert self.initialized
return self.h
def help(self):
"""
Description: Prints information about this class and its methods.
Args:
None
Returns:
None
"""
print(LDS_Control_help)
# string to print when calling help() method
LDS_Control_help = """
-------------------- *** --------------------
Id: LDS-Control-v0
Description: Simulates a linear dynamical system.
Methods:
initialize(n, m, d, noise=1.0)
Description:
Randomly initialize the hidden dynamics of the system.
Args:
n (int): Input dimension.
m (int): Observation/output dimension.
d (int): Hidden state dimension.
noise (float): Default value 1.0. The magnitude of the noise (Gaussian) added
to both the hidden state and the observable output.
Returns:
The first value in the time-series
step(u)
Description:
Moves the system dynamics one time-step forward.
Args:
u (numpy.ndarray): control input, an n-dimensional real-valued vector.
Returns:
A new observation from the LDS.
hidden()
Description:
Return the hidden state of the system.
Args:
None
Returns:
h: The hidden state of the LDS.
help()
Description:
Prints information about this class and its methods.
Args:
None
Returns:
None
-------------------- *** --------------------
"""