control.flatsys.BasisFamily

class control.flatsys.BasisFamily(N)

Bases: object

Base class for basis functions for flat systems.

A BasisFamily object is used to construct trajectories for a flat system. The class must implement a single function that computes the jth derivative of the ith basis function at a time t:

= basis.eval_deriv(self, i, j, t)

A basis set can either consist of a single variable that is used for each flat output (nvars = None) or a different variable for different flat outputs (nvars > 0).

Parameters

Nint

Order of the basis set.

Attributes

nvarsint or None

Number of variables represented by the basis (possibly of different order/length). Default is None (single variable).

coef_offsetlist

Coefficient offset for each variable.

coef_lengthlist

Coefficient length for each variable.

Methods

__call__	Evaluate the ith basis function at a point in time.
eval	Compute function values given the coefficients and time points.
eval_deriv	Evaluate kth derivative of ith basis function at time t.
var_ncoefs	Get the number of coefficients for a variable.

__call__(i, t, var=None)

Evaluate the ith basis function at a point in time.

eval(coeffs, tlist, var=None)

Compute function values given the coefficients and time points.

Parameters

coeffsarray

Basis function coefficient values.

tlistarray

List of times at which to evaluate the function.

varint or None, optional

Number of independent variables represented using the basis. If None, then basis represents a single variable.

Returns

array

Values of the variable(s) at the times in tlist.

eval_deriv(i, k, t, var=None)

Evaluate kth derivative of ith basis function at time t.

Parameters

iint

Basis function offset.

kint

Derivative order.

tfloat

Time at which to evaluating the derivative.

varint or None, optional

Variable offset.

Returns

float

var_ncoefs(var)

Get the number of coefficients for a variable.

Parameters

varint

Variable offset.

Returns

int