types.core.ControlInput

types.core.ControlInput

Unified type for control inputs to integration methods.

Allows flexible specification of control in numerical integration: - Constant control: Fixed array applied for all t - Time-varying control: Function u(t) evaluated at each time step
- Autonomous: None implies zero control

This type is primarily used in integration methods where the control strategy needs to be specified.

Type Variants

ControlVector : ArrayLike Constant control u(t) = u_const for all t ∈ [t0, tf] Shape: (nu,)

TimeVaryingControl : Callable[[float], ControlVector] Time-dependent control u(t) = u_func(t) Evaluated by integrator at each time point

None Zero control or autonomous dynamics Equivalent to u(t) = 0 for all t

Examples

Constant control:

>>> u_const = np.array([1.0, 0.5])
>>> result = system.integrate(x0, u=u_const, t_span=(0, 10))

Time-varying control:

>>> def u_func(t):
...     return np.array([np.sin(t), np.cos(t)])
>>> result = system.integrate(x0, u=u_func, t_span=(0, 10))

Autonomous (no control):

>>> result = system.integrate(x0, u=None, t_span=(0, 10))

Usage in Integration

The integration method handles each variant:

def integrate(self, x0: StateVector, u: ControlInput = None, …): … def rhs(t, x): … if u is None: … u_t = None … elif callable(u): … u_t = u(t) # Evaluate time-varying control … else: … u_t = u # Use constant control … return self(x, u_t, t)

Notes

For closed-loop simulation with state feedback, use FeedbackController in the simulate() method instead. ControlInput is for open-loop or pre-planned trajectories in integrate().

See Also

FeedbackController : Closed-loop control for simulate() TimeVaryingControl : Component type for time-varying control ControlVector : Component type for constant control

# types.core.ControlInput { #cdesym.types.core.ControlInput }

`types.core.ControlInput`

Unified type for control inputs to integration methods.

Allows flexible specification of control in numerical integration:
- Constant control: Fixed array applied for all t
- Time-varying control: Function u(t) evaluated at each time step  
- Autonomous: None implies zero control

This type is primarily used in integration methods where the control
strategy needs to be specified.

## Type Variants {.doc-section .doc-section-type-variants}

ControlVector : ArrayLike
    Constant control u(t) = u_const for all t ∈ [t0, tf]
    Shape: (nu,)

TimeVaryingControl : Callable[[float], ControlVector]
    Time-dependent control u(t) = u_func(t)
    Evaluated by integrator at each time point

None
    Zero control or autonomous dynamics
    Equivalent to u(t) = 0 for all t

## Examples {.doc-section .doc-section-examples}

Constant control:

```python
>>> u_const = np.array([1.0, 0.5])
>>> result = system.integrate(x0, u=u_const, t_span=(0, 10))
```

Time-varying control:

```python
>>> def u_func(t):
...     return np.array([np.sin(t), np.cos(t)])
>>> result = system.integrate(x0, u=u_func, t_span=(0, 10))
```

Autonomous (no control):

```python
>>> result = system.integrate(x0, u=None, t_span=(0, 10))
```

## Usage in Integration {.doc-section .doc-section-usage-in-integration}

The integration method handles each variant:

>>> def integrate(self, x0: StateVector, u: ControlInput = None, ...):
...     def rhs(t, x):
...         if u is None:
...             u_t = None
...         elif callable(u):
...             u_t = u(t)  # Evaluate time-varying control
...         else:
...             u_t = u     # Use constant control
...         return self(x, u_t, t)

## Notes {.doc-section .doc-section-notes}

For closed-loop simulation with state feedback, use FeedbackController
in the simulate() method instead. ControlInput is for open-loop or
pre-planned trajectories in integrate().

## See Also {.doc-section .doc-section-see-also}

FeedbackController : Closed-loop control for simulate()
TimeVaryingControl : Component type for time-varying control
ControlVector : Component type for constant control