types.core.DynamicsFunction

types.core.DynamicsFunction

Dynamics function f(x, u).

Continuous: f(x, u, t) → dx/dt (rate of change) Discrete: f(x, u) → x[k+1] (next state)

Parameters

Name	Type	Description	Default
x	StateVector	Current state (nx,)	required
u	Optional[ControlVector]	Control input (nu,) or None for autonomous	required

Returns

Name	Type	Description
	StateVector	Dynamics evaluation (nx,)

Examples

>>> # Linear dynamics
>>> def f_linear(x: StateVector, u: ControlVector) -> StateVector:
...     return A @ x + B @ u
>>> 
>>> # Nonlinear dynamics
>>> def f_nonlinear(x: StateVector, u: ControlVector) -> StateVector:
...     x1, x2 = x
...     return np.array([x2, -np.sin(x1) + u[0]])
>>> 
>>> # Autonomous
>>> def f_autonomous(x: StateVector, u: Optional[ControlVector] = None) -> StateVector:
...     return -alpha * x

# types.core.DynamicsFunction { #cdesym.types.core.DynamicsFunction }

`types.core.DynamicsFunction`

Dynamics function f(x, u).

Continuous: f(x, u, t) → dx/dt (rate of change)
Discrete: f(x, u) → x[k+1] (next state)

## Parameters {.doc-section .doc-section-parameters}

| Name   | Type                      | Description                                | Default    |
|--------|---------------------------|--------------------------------------------|------------|
| x      | StateVector               | Current state (nx,)                        | _required_ |
| u      | Optional\[ControlVector\] | Control input (nu,) or None for autonomous | _required_ |

## Returns {.doc-section .doc-section-returns}

| Name   | Type        | Description               |
|--------|-------------|---------------------------|
|        | StateVector | Dynamics evaluation (nx,) |

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

```python
>>> # Linear dynamics
>>> def f_linear(x: StateVector, u: ControlVector) -> StateVector:
...     return A @ x + B @ u
>>> 
>>> # Nonlinear dynamics
>>> def f_nonlinear(x: StateVector, u: ControlVector) -> StateVector:
...     x1, x2 = x
...     return np.array([x2, -np.sin(x1) + u[0]])
>>> 
>>> # Autonomous
>>> def f_autonomous(x: StateVector, u: Optional[ControlVector] = None) -> StateVector:
...     return -alpha * x
```