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add basis functions, solver options, examples/tests
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7 files changed

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‎control/flatsys/__init__.py

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@@ -53,6 +53,7 @@
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# Basis function families
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from .basis import BasisFamily
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from .poly import PolyFamily
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from .bezier import BezierFamily
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# Classes
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from .systraj import SystemTrajectory

‎control/flatsys/basis.py

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@@ -51,3 +51,10 @@ class BasisFamily:
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def __init__(self, N):
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"""Create a basis family of order N."""
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self.N = N # save number of basis functions
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def __call__(self, i, t):
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"""Evaluate the ith basis function at a point in time"""
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return self.eval_deriv(i, 0, t)
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def eval_deriv(self, i, j, t):
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raise NotImplementedError("Internal error; improper basis functions")

‎control/flatsys/bezier.py

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# bezier.m - 1D Bezier curve basis functions
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# RMM, 24 Feb 2021
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#
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# This class implements a set of basis functions based on Bezier curves:
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#
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# \phi_i(t) = \sum_{i=0}^n {n \choose i} (T - t)^{n-i} t^i
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#
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# Copyright (c) 2012 by California Institute of Technology
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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#
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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#
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# 2. Redistributions in binary form must reproduce the above copyright
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# notice, this list of conditions and the following disclaimer in the
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# documentation and/or other materials provided with the distribution.
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#
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# 3. Neither the name of the California Institute of Technology nor
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# the names of its contributors may be used to endorse or promote
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# products derived from this software without specific prior
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# written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CALTECH
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# OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
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# USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
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# OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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# SUCH DAMAGE.
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import numpy as np
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from scipy.special import binom
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from .basis import BasisFamily
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class BezierFamily(BasisFamily):
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r"""Polynomial basis functions.
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This class represents the family of polynomials of the form
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.. math::
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\phi_i(t) = \sum_{i=0}^n {n \choose i} (T - t)^{n-i} t^i
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"""
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def __init__(self, N, T=1):
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"""Create a polynomial basis of order N."""
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self.N = N # save number of basis functions
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self.T = T # save end of time interval
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# Compute the kth derivative of the ith basis function at time t
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def eval_deriv(self, i, k, t):
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"""Evaluate the kth derivative of the ith basis function at time t."""
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if k > 0:
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raise NotImplementedError("Bezier derivatives not yet available")
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elif i > self.N:
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raise ValueError("Basis function index too high")
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# Return the Bezier basis function (note N = # basis functions)
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return binom(self.N - 1, i) * \
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(t/self.T)**i * (1 - t/self.T)**(self.N - i - 1)

‎control/iosys.py

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@@ -1412,9 +1412,10 @@ def __init__(self, io_sys, ss_sys=None):
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raise TypeError("Second argument must be a state space system.")
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def input_output_response(sys, T, U=0., X0=0, params={}, method='RK45',
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transpose=False, return_x=False, squeeze=None):
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def input_output_response(
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sys, T, U=0., X0=0, params={},
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transpose=False, return_x=False, squeeze=None,
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solve_ivp_kwargs={}, **kwargs):
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"""Compute the output response of a system to a given input.
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Simulate a dynamical system with a given input and return its output
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ValueError
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If time step does not match sampling time (for discrete time systems)
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Additional parameters
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---------------------
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solve_ivp_method : str, optional
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Set the method used by :func:`scipy.integrate.solve_ivp`. Defaults
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to 'RK45'.
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solve_ivp_kwargs : str, optional
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Pass additional keywords to :func:`scipy.integrate.solve_ivp`.
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"""
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#
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# Process keyword arguments
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#
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# Allow method as an alternative to solve_ivp_method
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if kwargs.get('method', None):
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solve_ivp_kwargs['method'] = kwargs.pop('method')
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# Figure out the method to be used
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if kwargs.get('solve_ivp_method', None):
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if kwargs.get('method', None):
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raise ValueError("ivp_method specified more than once")
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solve_ivp_kwargs['method'] = kwargs['solve_ivp_method']
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# Set the default method to 'RK45'
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if solve_ivp_kwargs.get('method', None) is None:
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solve_ivp_kwargs['method'] = 'RK45'
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# Sanity checking on the input
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if not isinstance(sys, InputOutputSystem):
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raise TypeError("System of type ", type(sys), " not valid")
@@ -1504,8 +1531,9 @@ def ivp_rhs(t, x): return sys._rhs(t, x, u(t))
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if not hasattr(sp.integrate, 'solve_ivp'):
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raise NameError("scipy.integrate.solve_ivp not found; "
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"use SciPy 1.0 or greater")
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soln = sp.integrate.solve_ivp(ivp_rhs, (T0, Tf), X0, t_eval=T,
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method=method, vectorized=False)
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soln = sp.integrate.solve_ivp(
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ivp_rhs, (T0, Tf), X0, t_eval=T,
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vectorized=False, **solve_ivp_kwargs)
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# Compute the output associated with the state (and use sys.out to
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# figure out the number of outputs just in case it wasn't specified)

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