types.core.FeedbackController

types.core.FeedbackController

Feedback controller with time awareness π(x, t).

Maps (state, time) to control action: u = π(x, t).

This generalizes ControlPolicy to include explicit time-dependence, allowing for time-varying gains, scheduled controllers, or reference tracking with time-varying setpoints.

Parameters

Name	Type	Description	Default
x	StateVector	Current state (nx,)	required
t	float	Current time	required

Returns

Name	Type	Description
	ControlVector	Control action (nu,)

Examples

>>> # Time-varying LQR (scheduled gain)
>>> def scheduled_lqr(x: StateVector, t: float) -> ControlVector:
...     K_t = K0 * np.exp(-t / tau)  # Decaying gain
...     return -K_t @ x
>>> 
>>> # Reference tracking with time-varying setpoint
>>> def tracking_controller(x: StateVector, t: float) -> ControlVector:
...     x_ref_t = np.array([np.sin(t), np.cos(t)])
...     error = x - x_ref_t
...     return -K @ error
>>> 
>>> # Gain scheduling based on time
>>> def gain_scheduled(x: StateVector, t: float) -> ControlVector:
...     if t < 5.0:
...         return -K_low @ x   # Low gain initially
...     else:
...         return -K_high @ x  # High gain later
>>> 
>>> # Model predictive control with receding horizon
>>> def mpc_controller(x: StateVector, t: float) -> ControlVector:
...     horizon = [t, t + T_horizon]
...     return solve_mpc(x, horizon)
>>> 
>>> # Use in simulation
>>> result = system.simulate(x0, controller=tracking_controller, t_span=(0, 10))

Notes

For purely state-dependent control (no time dependence), prefer ControlPolicy which has the simpler signature u = π(x).

See Also

ControlPolicy : Pure state feedback u = π(x) TimeVaryingControl : Pure time-varying u = u(t)