gncpy.math.get_input_jacobian

get_input_jacobian(t, x, u, fncs, f_args, **kwargs)

Calculates the jacobian matrix for the input of a state space model.

Notes

Numerically calculates the jacobian using the central difference method for the input of the standard statespace model

\[\dot{x} = f(t, x, u)\]

Parameters:

• t (float) – timestep to evaluate at.

• x (N x 1 numpy array) – state to calculate the jocobain about.

• u (Nu x 1 numpy array) – control input to calculate the jocobian about.

• fncs (list) – 1 function per state in order. They must have the signature f(t, x, u, *f_args) if u is given or f(t, x, *f_args) if u is not given.

• f_args (tuple) – Additional arguemnts to pass to each function in fncs.

• **kwargs (dict, optional) – Additional keyword arguments for gncpy.math.get_jacobian().

Returns:

jac – jacobian matrix.

Return type:

N x Nu numpy array