# Copyright 2020 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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"""deluca.agents._lqr"""
import jax.numpy as jnp
from scipy.linalg import solve_discrete_are as dare
from deluca.agents.core import Agent
# TODO: need to address problem of LQR with jax.lax.scan
[docs]class LQR(Agent):
"""
LQR
"""
[docs] def __init__(
self, A: jnp.ndarray, B: jnp.ndarray, Q: jnp.ndarray = None, R: jnp.ndarray = None
) -> None:
"""
Description: Initialize the infinite-time horizon LQR.
Args:
A (jnp.ndarray): system dynamics
B (jnp.ndarray): system dynamics
Q (jnp.ndarray): cost matrices (i.e. cost = x^TQx + u^TRu)
R (jnp.ndarray): cost matrices (i.e. cost = x^TQx + u^TRu)
Returns:
None
"""
state_size, action_size = B.shape
if Q is None:
Q = jnp.identity(state_size, dtype=jnp.float32)
if R is None:
R = jnp.identity(action_size, dtype=jnp.float32)
# solve the ricatti equation
X = dare(A, B, Q, R)
# compute LQR gain
self.K = jnp.linalg.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
[docs] def __call__(self, state) -> jnp.ndarray:
"""
Description: Return the action based on current state and internal parameters.
Args:
state (float/numpy.ndarray): current state
Returns:
jnp.ndarray: action to take
"""
return -self.K @ state