Dynamical systems

feedbax.dynamics.LTISystem (AbstractDynamicalSystem[Array])

Inspired by this Diffrax example.

A linear, continuous, time-invariant system.

Attributes:

Name	Type	Description
A	Float[Array, 'state state']	The state evolution matrix.
B	Float[Array, 'state input']	The control matrix.
C	Float[Array, 'obs state']	The observation matrix.

input_size: int property

Number of control variables.

state_size: int property

Number of state variables.

vector_field (t: Scalar,state: Array,input: Array) -> Array

Returns time derivatives of the system's states.

init (*,key: Optional[PRNGKeyArray] = None) -> Array

Return a default state for the linear system.

Abstract base classes

feedbax.dynamics.AbstractDynamicalSystem (AbstractModel[StateT])

Base class for continuous dynamical systems.

Development note

The signature of vector_field matches that expected by diffrax.ODETerm. However, the argument that is called args in the Diffrax documentation, we call input, since we use it for input signals (e.g. forces from the controller)

Vector fields for biomechanical models are generally not time-dependent. That is, the argument t to vector_field is typically unused. This is apparent in the way we alias vector_field to __call__, which is a method that AbstractModel requires.

Perhaps it is unnecessary to inherit from AbstractModel, though.

vector_field (t: Scalar,state: StateT,input: PyTree[Array]) -> StateT

abstractmethod

Returns scalar (e.g. time) derivatives of the system's states.

init (*,key: PRNGKeyArray) -> StateT

abstractmethod

Returns the initial state of the system.

input_size () -> int

Number of input variables.

__call__ (input: PyTree[Array],state: StateT,key: PRNGKeyArray) -> StateT

Alias for vector_field, with a modified signature.