types.core.GainMatrix

types.core.GainMatrix

Gain matrix for control or estimation.

Maps state/output to control/estimate.

Uses: - LQR gain: K (nu, nx) where u = -Kx - Kalman gain: L (nx, ny) where x̂̇ = … + L(y - C*x̂) - Observer gain: K_obs (nx, ny)

Examples

>>> # LQR feedback gain
>>> K_lqr: GainMatrix = np.array([[1.0, 0.5]])  # (nu=1, nx=2)
>>> u = -K_lqr @ x
>>> 
>>> # Kalman gain
>>> K_kalman: GainMatrix = np.array([[0.1], [0.2]])  # (nx=2, ny=1)
>>> innovation = y - C @ x_hat
>>> x_hat_update = x_hat + K_kalman @ innovation