feat(v0.3): state observers — Kalman filter and Luenberger observer

[Oseiasdfarias]

Overview

Add state estimation to synapsys.observers — the missing piece for output-feedback control loops where full state measurement is unavailable.

Classes

LuenbergerObserver

• Continuous and discrete variants
• Pole placement for observer gain L via place()
• predict(u) + update(y) interface

KalmanFilter

• Discrete Linear Kalman Filter (LKF)
• Process noise covariance Q, measurement noise covariance R
• predict(u) + update(y) → returns (x_hat, P)

ExtendedKalmanFilter (stretch goal)

• Linearises nonlinear dynamics at each step

Usage

from synapsys.observers import KalmanFilter, LuenbergerObserver

kf = KalmanFilter(A, B, C, Q=np.eye(4)*0.01, R=np.eye(2)*0.1)
kf.predict(u)
x_hat, P = kf.update(y_measured)

obs = LuenbergerObserver(A, B, C, poles=[-10, -10, -12, -12])
obs.predict(u)
x_hat = obs.update(y_measured)

Acceptance Criteria

• LKF validated on cart-pole simulator (vs. ground-truth state)
• Luenberger validated on DC motor simulator
• 100% test coverage, mypy strict
• Integration example with ControllerAgent