state_space module

class dynamapp.state_space.StateSpace(a: jax.numpy.ndarray, b: jax.numpy.ndarray, c: jax.numpy.ndarray, d: jax.numpy.ndarray, k: jax.numpy.ndarray = None, x_init: jax.numpy.ndarray = None, y_column_names: List[str] = None, u_column_names: List[str] = None)

Bases: object

A state-space model defined by the following equations:

\[\begin{split}\begin{cases} x_{k+1} &= A x_k + B u_k + K e_k \\ y_k &= C x_k + D u_k + e_k \end{cases}\end{split}\]

The shapes of the matrices are checked for consistency and will raise if inconsistent. If a matrix does not exist in the model representation, the corresponding jnp.ndarray should have dimension zero along that axis. See the example below.

Example

An autonomous state-space model has no matrices \(B\) and \(D\). An autonomous model with a one-dimensional internal state and output, can be represented as follows:

>>> model = StateSpace(
>>>     jnp.ones((1, 1)),
>>>     jnp.ones((1, 0)),
>>>     jnp.ones((1, 1)),
>>>     jnp.ones((1, 0))
>>> )

param a:

matrix \(A\)

param b:

matrix \(B\)

param c:

matrix \(C\)

param d:

matrix \(D\)

param k:

matrix \(K\), optional

param x_init:

initial state \(x_0\) of the model, optional

param y_column_names:

list of output column names, optional

param u_column_names:

list of input column names, optional

set_matrices(a: jax.numpy.ndarray, b: jax.numpy.ndarray, c: jax.numpy.ndarray, d: jax.numpy.ndarray, k: jax.numpy.ndarray = None)

Validate if the shapes make sense and set the system matrices.

set_x_init(x_init: jax.numpy.ndarray)

Set the initial state, if it is given.

step(u: jax.numpy.ndarray = None, e: jax.numpy.ndarray = None) → jax.numpy.ndarray

Calculates the output of the state-space model and returns it. Updates the internal state of the model as well. The input u is optional, as is the noise e.

output(x: jax.numpy.ndarray, u: jax.numpy.ndarray = None, e: jax.numpy.ndarray = None)

Calculate the output of the state-space model. This function calculates the updated \(y_k\) of the state-space model in the class description. The current state x is required. Providing an input u is optional. Providing a noise term e to be added is optional as well.

to_dataframe() → pandas.DataFrame

Return the inputs and outputs of the state-space model as a dataframe, where the columns are the input- and output-columns.