control.nlsys(updfcn, outfcn=None, inputs=None, outputs=None, states=None, **kwargs)[source]

Create a nonlinear input/output system.

Creates an InputOutputSystem for a nonlinear system by specifying a state update function and an output function. The new system can be a continuous or discrete time system.

  • updfcn (callable) –

    Function returning the state update function

    updfcn(t, x, u, params) -> array

    where x is a 1-D array with shape (nstates,), u is a 1-D array with shape (ninputs,), t is a float representing the currrent time, and params is a dict containing the values of parameters used by the function.

  • outfcn (callable) –

    Function returning the output at the given state

    outfcn(t, x, u, params) -> array

    where the arguments are the same as for upfcn.

  • inputs (int, list of str or None, optional) – Description of the system inputs. This can be given as an integer count or as a list of strings that name the individual signals. If an integer count is specified, the names of the signal will be of the form s[i] (where s is one of u, y, or x). If this parameter is not given or given as None, the relevant quantity will be determined when possible based on other information provided to functions using the system.

  • outputs (int, list of str or None, optional) – Description of the system outputs. Same format as inputs.

  • states (int, list of str, or None, optional) – Description of the system states. Same format as inputs.

  • dt (timebase, optional) –

    The timebase for the system, used to specify whether the system is operating in continuous or discrete time. It can have the following values:

    • dt = 0: continuous time system (default)

    • dt > 0: discrete time system with sampling period ‘dt’

    • dt = True: discrete time with unspecified sampling period

    • dt = None: no timebase specified

  • name (string, optional) – System name (used for specifying signals). If unspecified, a generic name <sys[id]> is generated with a unique integer id.

  • params (dict, optional) – Parameter values for the systems. Passed to the evaluation functions for the system as default values, overriding internal defaults.


sys – Nonlinear input/output system.

Return type


See also

ss, tf


>>> def kincar_update(t, x, u, params):
...     l = params.get('l', 1)  # wheelbase
...     return np.array([
...         np.cos(x[2]) * u[0],     # x velocity
...         np.sin(x[2]) * u[0],     # y velocity
...         np.tan(u[1]) * u[0] / l  # angular velocity
...     ])
>>> def kincar_output(t, x, u, params):
...     return x[0:2]  # x, y position
>>> kincar = ct.nlsys(
...     kincar_update, kincar_output, states=3, inputs=2, outputs=2)
>>> timepts = np.linspace(0, 10)
>>> response = ct.input_output_response(
...     kincar, timepts, [10, 0.05 * np.sin(timepts)])