Jul 2, 2023 · Jun 20, 2023 · Jun 20, 2023 · Jun 20, 2023 · Jun 20, 2023 · Jun 20, 2023
diff --git a/control/__init__.py b/control/__init__.py
 Available subpackages
 ---------------------

 The main control package includes the mostcommpon functions used in
 The main control package includes the mostcommon functions used in
 analysis, design, and simulation of feedback control systems.  Several
 additional subpackages are available that provide more specialized
 functionality:
diff --git a/doc/conf.py b/doc/conf.py
 # -- Project information -----------------------------------------------------

 project = u'Python Control Systems Library'
 copyright = u'2022, python-control.org'
 copyright = u'2023, python-control.org'
 author = u'Python Control Developers'

 # Version information - read from the source code
diff --git a/doc/conventions.rst b/doc/conventions.rst

 Linear time invariant (LTI) systems are represented in python-control in
 state space, transfer function, or frequency response data (FRD) form.  Most
 functions in the toolbox will operate on any of these data types and
 functions for converting between compatible typesis provided.
 functions in the toolbox will operate on any of these data types, and
 functions for converting between compatible typesare provided.

 State space systems
 -------------------

 The :func:`forced_response` system is the most general and allows by
 the zero initial state response to be simulated as well as the
 response from a non-zerointial condition.
 response from a non-zeroinitial condition.

 In addition the :func:`input_output_response` function, which handles
 simulation of nonlinear systems and interconnected systems, can be
diff --git a/doc/examples.rst b/doc/examples.rst
 ********

 The source code for the examples below are available in the `examples/`
 subdirecory of the source code distribution. The can also be accessed online
 subdirectory of the source code distribution.They can also be accessed online
 via the [python-control GitHub repository](https://github.com/python-control/python-control/tree/master/examples).


 =================

 The examples below use `python-control` in a Jupyter notebook environment.
 These notebooks demonstrate the use of modeling,anaylsis, and design tools
 These notebooks demonstrate the use of modeling,analysis, and design tools
 using examples from textbooks
 (`FBS <https://fbswiki.org/wiki/index.php?title=FBS>`_,
 `OBC <https://fbswiki.org/wiki/index.php?title=OBC>`_), courses, and other
diff --git a/doc/flatsys.rst b/doc/flatsys.rst
 trajectory generation is required. Since the behavior of a flat system
 is determined by the flat outputs, we can plan trajectories in output
 space, and then map these to appropriate inputs.  Suppose we wish to
 generate a feasible trajectory for thethenonlinear system
 generate a feasible trajectory for the nonlinear system

 .. math::
    \dot x = f(x, u), \qquad x(0) = x_0,\, x(T) = x_f.
    traj = control.flatsys.solve_flat_ocp(
        sys, timepts, x0, u0, cost, basis=basis)

 The `cost` parameter is a functionfunctionwith call signature
 The `cost` parameter is a function with call signature
 `cost(x, u)` and should return the (incremental) cost at the given
 state, and input.  It will be evaluated at each point in the `timepts`
 vector.  The `terminal_cost` parameter can be used to specify a cost
 To illustrate how we can use a two degree-of-freedom design to improve the
 performance of the system, consider the problem of steering a car to change
 lanes on a road. We use the non-normalized form of the dynamics, which are
 derived *Feedback Systems* by Astrom and Murray, Example 3.11.
 derivedin*Feedback Systems* by Astrom and Murray, Example 3.11.

 .. code-block:: python

diff --git a/doc/interconnect_tutorial.ipynb b/doc/interconnect_tutorial.ipynb
 ../examples/interconnect_tutorial.ipynb
diff --git a/doc/intro.rst b/doc/intro.rst
 <https://docs.scipy.org/doc/numpy/user/numpy-for-matlab-users.html>`_.

 In terms of the python-control package more specifically, here are
 something to keep in mind:
 somethings to keep in mind:

 * You must include commas in vectors.  So [1 2 3] must be [1, 2, 3].
 * Functions that return multiple arguments use tuples.
 .. note::
   Mixing packages from conda-forge and the default conda channel
   can sometimes cause problems with dependencies, so it is usually best to
   instally NumPy, SciPy, and Matplotlib from conda-forge as well.)
   instally NumPy, SciPy, and Matplotlib from conda-forge as well.

 To install using pip::

diff --git a/doc/iosys.rst b/doc/iosys.rst
 If a signal name appears in multiple outputs then that signal will be summed
 when it is interconnected.  Similarly, if a signal name appears in multiple
 inputs then all systems using that signal name will receive the same input.
 The :func:`~control.interconnect` function will generate an error ifan signal
 The :func:`~control.interconnect` function will generate an error ifa signal
 listed in ``inplist`` or ``outlist`` (corresponding to the inputs and outputs
 of the interconnected system) is not found, but inputs and outputs of
 individual systems that are not connected to other systems are left
 the estimator.

 Integral action can be included using the `integral_action` keyword.
 The value of this keyword can either bean matrix (ndarray) or a
 The value of this keyword can either bea matrix (ndarray) or a
 function.  If a matrix :math:`C` is specified, the difference between
 the desired state and system state will be multiplied by this matrix
 and integrated.  The controller gain should then consist of a set of
diff --git a/doc/optimal.rst b/doc/optimal.rst
 previous :math:`N` steps in time, including the "current" time
 :math:`x[N]`.  The basic idea is thus to compute the state estimate that is
 most consistent with our model and penalize the noise and disturbances
 according to how likelythe are (based on the given stochastic system
 according to how likelythey are (based on the given stochastic system
 model for each).

 Given a solution to this fixed-horizon optimal estimation problem, we can

 We consider an optimal control problem that consists of "changing lanes" by
 moving from the point x = 0 m, y = -2 m, :math:`\theta` = 0 to the point x =
 100 m, y = 2 m, :math:`\theta` = 0) over a period of 10 seconds and with a
 100 m, y = 2 m, :math:`\theta` = 0) over a period of 10 seconds and
 with a starting and ending velocity of 10 m/s::

  x0 = np.array([0., -2., 0.]); u0 = np.array([10., 0.])
  traj_cost = obc.quadratic_cost(vehicle, Q, R, x0=xf, u0=uf)
  term_cost = obc.quadratic_cost(vehicle, P, 0, x0=xf)

 We alsoconstraint the maximum turning rate to 0.1 radians (about 6degees)
 We alsoconstrain the maximum turning rate to 0.1 radians (about 6degrees)
 and constrain the velocity to be in the range of 9 m/s to 11 m/s::

  constraints = [ obc.input_range_constraint(vehicle, [8, -0.1], [12, 0.1]) ]
  good solutions with a small number of free variables (the example above
  uses 3 time points for 2 inputs, so a total of 6 optimization variables).
  Note that you can "resample" the optimal trajectory by running a
  simulation of thesytem and using the `t_eval` keyword in
  simulation of thesystem and using the `t_eval` keyword in
  `input_output_response` (as done above).

 * Use a smooth basis: as an alternative to parameterizing the optimal
  and `minimize_kwargs` keywords in :func:`~control.solve_ocp`, you can
  choose the SciPy optimization function that you use and set many
  parameters.  See :func:`scipy.optimize.minimize` for more information on
  theoptimzers that are available and the options and keywords that they
  theoptimizers that are available and the options and keywords that they
  accept.

 * Walk before you run: try setting up a simpler version of the optimization,
  remove constraints or simplifying the cost to get a simple version of the
  problem working and then add complexity.  Sometimes this can help you find
  the right set of options or identify situations in which you are being too
  aggressive in whatyour are trying to get the system to do.
  aggressive in whatyou are trying to get the system to do.

 See :ref:`steering-optimal` for some examples of different problem
 formulations.
diff --git a/doc/simulating_discrete_nonlinear.ipynb b/doc/simulating_discrete_nonlinear.ipynb
 ../examples/simulating_discrete_nonlinear.ipynb
diff --git a/doc/steering-optimal.rst b/doc/steering-optimal.rst
 .. _steering-optimal:

 Optimal control for vehiclesteeering (lane change)
 Optimal control for vehiclesteering (lane change)
 ---------------------------------------------------

 Code
Original file line number	Diff line number	Diff line change
Expand Up		@@ -55,7 +55,7 @@
		Available subpackages
		---------------------

		The main control package includes the mostcommpon functions used in
		The main control package includes the mostcommon functions used in
		analysis, design, and simulation of feedback control systems. Several
		additional subpackages are available that provide more specialized
		functionality:
Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -30,7 +30,7 @@
		# -- Project information -----------------------------------------------------

		project = u'Python Control Systems Library'
		copyright = u'2022, python-control.org'
		copyright = u'2023, python-control.org'
		author = u'Python Control Developers'

		# Version information - read from the source code
Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -16,8 +16,8 @@ LTI system representation

		Linear time invariant (LTI) systems are represented in python-control in
		state space, transfer function, or frequency response data (FRD) form. Most
		functions in the toolbox will operate on any of these data types and
		functions for converting between compatible typesis provided.
		functions in the toolbox will operate on any of these data types, and
		functions for converting between compatible typesare provided.

		State space systems
		-------------------
Expand DownExpand Up		@@ -152,7 +152,7 @@ in the next section).

		The :func:`forced_response` system is the most general and allows by
		the zero initial state response to be simulated as well as the
		response from a non-zerointial condition.
		response from a non-zeroinitial condition.

		In addition the :func:`input_output_response` function, which handles
		simulation of nonlinear systems and interconnected systems, can be
Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -6,7 +6,7 @@ Examples
		********

		The source code for the examples below are available in the `examples/`
		subdirecory of the source code distribution. The can also be accessed online
		subdirectory of the source code distribution.They can also be accessed online
		via the [python-control GitHub repository](https://github.com/python-control/python-control/tree/master/examples).


Expand DownExpand Up		@@ -38,7 +38,7 @@ Jupyter notebooks
		=================

		The examples below use `python-control` in a Jupyter notebook environment.
		These notebooks demonstrate the use of modeling,anaylsis, and design tools
		These notebooks demonstrate the use of modeling,analysis, and design tools
		using examples from textbooks
		(`FBS <https://fbswiki.org/wiki/index.php?title=FBS>`_,
		`OBC <https://fbswiki.org/wiki/index.php?title=OBC>`_), courses, and other
Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -39,7 +39,7 @@ Differentially flat systems are useful in situations where explicit
		trajectory generation is required. Since the behavior of a flat system
		is determined by the flat outputs, we can plan trajectories in output
		space, and then map these to appropriate inputs. Suppose we wish to
		generate a feasible trajectory for thethenonlinear system
		generate a feasible trajectory for the nonlinear system

		.. math::
		\dot x = f(x, u), \qquad x(0) = x_0,\, x(T) = x_f.
Expand DownExpand Up		@@ -181,7 +181,7 @@ solve an optimal control problem without a final state::
		traj = control.flatsys.solve_flat_ocp(
		sys, timepts, x0, u0, cost, basis=basis)

		The `cost` parameter is a functionfunctionwith call signature
		The `cost` parameter is a function with call signature
		`cost(x, u)` and should return the (incremental) cost at the given
		state, and input. It will be evaluated at each point in the `timepts`
		vector. The `terminal_cost` parameter can be used to specify a cost
Expand All		@@ -193,7 +193,7 @@ Example
		To illustrate how we can use a two degree-of-freedom design to improve the
		performance of the system, consider the problem of steering a car to change
		lanes on a road. We use the non-normalized form of the dynamics, which are
		derived Feedback Systems by Astrom and Murray, Example 3.11.
		derivedinFeedback Systems by Astrom and Murray, Example 3.11.

		.. code-block:: python

Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -26,7 +26,7 @@ NumPy and MATLAB can be found `here
		<https://docs.scipy.org/doc/numpy/user/numpy-for-matlab-users.html>`_.

		In terms of the python-control package more specifically, here are
		something to keep in mind:
		somethings to keep in mind:

		* You must include commas in vectors. So [1 2 3] must be [1, 2, 3].
		* Functions that return multiple arguments use tuples.
Expand DownExpand Up		@@ -56,7 +56,7 @@ they are not already present.
		.. note::
		Mixing packages from conda-forge and the default conda channel
		can sometimes cause problems with dependencies, so it is usually best to
		instally NumPy, SciPy, and Matplotlib from conda-forge as well.)
		instally NumPy, SciPy, and Matplotlib from conda-forge as well.

		To install using pip::

Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -251,7 +251,7 @@ will create a unity gain, negative feedback system::
		If a signal name appears in multiple outputs then that signal will be summed
		when it is interconnected. Similarly, if a signal name appears in multiple
		inputs then all systems using that signal name will receive the same input.
		The :func:`~control.interconnect` function will generate an error ifan signal
		The :func:`~control.interconnect` function will generate an error ifa signal
		listed in ``inplist`` or ``outlist`` (corresponding to the inputs and outputs
		of the interconnected system) is not found, but inputs and outputs of
		individual systems that are not connected to other systems are left
Expand DownExpand Up		@@ -404,7 +404,7 @@ The closed loop controller will include both the state feedback and
		the estimator.

		Integral action can be included using the `integral_action` keyword.
		The value of this keyword can either bean matrix (ndarray) or a
		The value of this keyword can either bea matrix (ndarray) or a
		function. If a matrix :math:`C` is specified, the difference between
		the desired state and system state will be multiplied by this matrix
		and integrated. The controller gain should then consist of a set of
Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -129,7 +129,7 @@ The result of this optimization gives us the estimated state for the
		previous :math:`N` steps in time, including the "current" time
		:math:`x[N]`. The basic idea is thus to compute the state estimate that is
		most consistent with our model and penalize the noise and disturbances
		according to how likelythe are (based on the given stochastic system
		according to how likelythey are (based on the given stochastic system
		model for each).

		Given a solution to this fixed-horizon optimal estimation problem, we can
Expand DownExpand Up		@@ -344,7 +344,7 @@ following code::

		We consider an optimal control problem that consists of "changing lanes" by
		moving from the point x = 0 m, y = -2 m, :math:`\theta` = 0 to the point x =
		100 m, y = 2 m, :math:`\theta` = 0) over a period of 10 seconds and with a
		100 m, y = 2 m, :math:`\theta` = 0) over a period of 10 seconds and
		with a starting and ending velocity of 10 m/s::

		x0 = np.array([0., -2., 0.]); u0 = np.array([10., 0.])
Expand All		@@ -360,7 +360,7 @@ penalizes the state and input using quadratic cost functions::
		traj_cost = obc.quadratic_cost(vehicle, Q, R, x0=xf, u0=uf)
		term_cost = obc.quadratic_cost(vehicle, P, 0, x0=xf)

		We alsoconstraint the maximum turning rate to 0.1 radians (about 6degees)
		We alsoconstrain the maximum turning rate to 0.1 radians (about 6degrees)
		and constrain the velocity to be in the range of 9 m/s to 11 m/s::

		constraints = [ obc.input_range_constraint(vehicle, [8, -0.1], [12, 0.1]) ]
Expand DownExpand Up		@@ -431,7 +431,7 @@ solutions do not seem close to optimal, here are a few things to try:
		good solutions with a small number of free variables (the example above
		uses 3 time points for 2 inputs, so a total of 6 optimization variables).
		Note that you can "resample" the optimal trajectory by running a
		simulation of thesytem and using the `t_eval` keyword in
		simulation of thesystem and using the `t_eval` keyword in
		`input_output_response` (as done above).

		* Use a smooth basis: as an alternative to parameterizing the optimal
Expand All		@@ -445,14 +445,14 @@ solutions do not seem close to optimal, here are a few things to try:
		and `minimize_kwargs` keywords in :func:`~control.solve_ocp`, you can
		choose the SciPy optimization function that you use and set many
		parameters. See :func:`scipy.optimize.minimize` for more information on
		theoptimzers that are available and the options and keywords that they
		theoptimizers that are available and the options and keywords that they
		accept.

		* Walk before you run: try setting up a simpler version of the optimization,
		remove constraints or simplifying the cost to get a simple version of the
		problem working and then add complexity. Sometimes this can help you find
		the right set of options or identify situations in which you are being too
		aggressive in whatyour are trying to get the system to do.
		aggressive in whatyou are trying to get the system to do.

		See :ref:`steering-optimal` for some examples of different problem
		formulations.
Expand Down
Original file line number	Diff line number	Diff line change
		@@ -0,0 +1 @@
		../examples/simulating_discrete_nonlinear.ipynb
Original file line number	Diff line number	Diff line change
		@@ -1,6 +1,6 @@
		.. _steering-optimal:

		Optimal control for vehiclesteeering (lane change)
		Optimal control for vehiclesteering (lane change)
		---------------------------------------------------

		Code
Expand Down