Computes the linearization of a general non-linear ControlledSystem using numerical differentiation. More...

#include <SystemLinearizer.h>

Inheritance diagram for ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >:

Public Types
typedef Base::time_t	time_t
	Time type as defined in System. More...

typedef Base::state_vector_t	state_vector_t
	state vector type More...

typedef Base::control_vector_t	control_vector_t
	input vector type More...

typedef Base::state_matrix_t	state_matrix_t
	state Jacobian type More...

typedef Base::state_control_matrix_t	state_control_matrix_t
	input Jacobian type More...

typedef ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >	system_t
	type of system to be linearized More...

Public Types inherited from ct::core::LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >
typedef Base::time_t	time_t

typedef StateVector< STATE_DIM, SCALAR >	state_vector_t
	state vector type More...

typedef ControlVector< CONTROL_DIM, SCALAR >	control_vector_t
	input vector type More...

typedef StateMatrix< STATE_DIM, SCALAR >	state_matrix_t
	state Jacobian type More...

typedef StateControlMatrix< STATE_DIM, CONTROL_DIM, SCALAR >	state_control_matrix_t
	input Jacobian type More...

Public Types inherited from ct::core::ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >
typedef std::shared_ptr< ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR > >	Ptr

typedef Base::time_t	time_t

Public Types inherited from ct::core::System< STATE_DIM, SCALAR >
typedef SCALAR	time_t
	the type of the time variable More...

Public Member Functions
	SystemLinearizer (std::shared_ptr< system_t > nonlinearSystem, bool doubleSidedDerivative=true)
	default constructor More...

	SystemLinearizer (const SystemLinearizer &arg)
	copy constructor More...

virtual	~SystemLinearizer ()
	destructor More...

SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR > *	clone () const override
	deep cloning More...

virtual const state_matrix_t &	getDerivativeState (const state_vector_t &x, const control_vector_t &u, const time_t t=0.0) override
	get the Jacobian with respect to the state More...

virtual const state_control_matrix_t &	getDerivativeControl (const state_vector_t &x, const control_vector_t &u, const time_t t=0.0) override
	get the Jacobian with respect to the input More...

Public Member Functions inherited from ct::core::LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >
	LinearSystem (const ct::core::SYSTEM_TYPE &type=ct::core::SYSTEM_TYPE::GENERAL)
	default constructor More...

virtual	~LinearSystem ()
	destructor More...

virtual void	computeControlledDynamics (const state_vector_t &state, const time_t &t, const control_vector_t &control, state_vector_t &derivative) override
	compute the system dynamics More...

virtual void	getDerivatives (state_matrix_t &A, state_control_matrix_t &B, const state_vector_t &x, const control_vector_t &u, const time_t t=time_t(0.0))
	Get both linear system matrices A and B in one call. More...

Public Member Functions inherited from ct::core::ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >
	ControlledSystem (const SYSTEM_TYPE &type=SYSTEM_TYPE::GENERAL)
	default constructor More...

	ControlledSystem (std::shared_ptr< ct::core::Controller< STATE_DIM, CONTROL_DIM, SCALAR >> controller, const SYSTEM_TYPE &type=SYSTEM_TYPE::GENERAL)
	constructor More...

	ControlledSystem (const ControlledSystem &arg)
	copy constructor More...

virtual	~ControlledSystem ()
	destructor More...

void	setController (const std::shared_ptr< Controller< STATE_DIM, CONTROL_DIM, SCALAR >> &controller)
	set a new controller More...

void	getController (std::shared_ptr< Controller< STATE_DIM, CONTROL_DIM, SCALAR >> &controller) const
	get the controller instance More...

std::shared_ptr< Controller< STATE_DIM, CONTROL_DIM, SCALAR > >	getController ()
	get the controller instace More...

virtual void	computeDynamics (const StateVector< STATE_DIM, SCALAR > &state, const time_t &t, StateVector< STATE_DIM, SCALAR > &derivative) override
	compute the dynamics of the system More...

virtual void	computeControlledDynamics (const StateVector< STATE_DIM, SCALAR > &state, const time_t &t, const ControlVector< CONTROL_DIM, SCALAR > &control, StateVector< STATE_DIM, SCALAR > &derivative)=0

ControlVector< CONTROL_DIM, SCALAR >	getLastControlAction ()

Public Member Functions inherited from ct::core::System< STATE_DIM, SCALAR >
	System (const SYSTEM_TYPE &type=SYSTEM_TYPE::GENERAL)
	default constructor More...

	System (const System &other)
	copy constructor More...

virtual	~System ()
	destructor More...

virtual void	computeDynamics (const StateVector< STATE_DIM, SCALAR > &state, const time_t &t, StateVector< STATE_DIM, SCALAR > &derivative)=0
	computes the system dynamics More...

SYSTEM_TYPE	getType () const
	get the type of system More...

virtual bool	isSymplectic () const
	Determines if the system is in symplectic form. More...

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >	Base
	Base class type. More...

Public Attributes inherited from ct::core::LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >	Base

Public Attributes inherited from ct::core::ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef System< STATE_DIM, SCALAR >	Base

Public Attributes inherited from ct::core::System< STATE_DIM, SCALAR >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef SCALAR	S
	the scalar type More...

Protected Attributes
std::shared_ptr< system_t >	nonlinearSystem_
	instance of non-linear system More...

DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, SCALAR >	linearizer_
	instance of numerical-linearizer More...

state_matrix_t	dFdx_
	Jacobian wrt state. More...

state_control_matrix_t	dFdu_
	Jacobian wrt input. More...

bool	isSecondOrderSystem_
	flag if system is a second order system More...

Protected Attributes inherited from ct::core::ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >
std::shared_ptr< Controller< STATE_DIM, CONTROL_DIM, SCALAR > >	controller_
	the controller instance More...

ControlVector< CONTROL_DIM, SCALAR >	controlAction_

Protected Attributes inherited from ct::core::System< STATE_DIM, SCALAR >
SYSTEM_TYPE	type_
	type of system More...

Detailed Description

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>
class ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >

Computes the linearization of a general non-linear ControlledSystem using numerical differentiation.

This class takes a non-linear ControlledSystem $\dot{x} = f(x,u,t)$ and computes the linearization around a certain point $ x = x_s $ , $ u = u_s $ .

$\dot{x} = A x + B u$

where

$\begin{aligned} A &= \frac{df}{dx} |_{x=x_s, u=u_s} \\ B &= \frac{df}{du} |_{x=x_s, u=u_s} \end{aligned}$

In case the ControlledSystem is a pure second-order system, the upper half of A is not explicitely computed but A is assumed to be of the following form

$A = \begin{bmatrix} 0 & I \\ ... & ... \end{bmatrix}$

Examples for using the SystemLinearizer (and the Auto-diff Linearizer) can be found in AutoDiffLinearizerTest.cpp

Note: In case your ControlledSystem is templated on scalar type, we suggest using the ADCodegenLinearizer for highest efficiency and accuracy. If this is not the case but your system is a RigidBodySystem you can fall back to the ct::rbd::RBDLinearizer for good accuracy and speed.

Template Parameters

STATE_DIM	dimension of state vector
CONTROL_DIM	dimension of control vector
SCALAR	underlying scalar type of the system

Examples:: AutoDiffLinearizerTest.cpp.

Member Typedef Documentation

◆ time_t

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

typedef Base::time_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::time_t

Time type as defined in System.

◆ state_vector_t

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

typedef Base::state_vector_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::state_vector_t

state vector type

◆ control_vector_t

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

typedef Base::control_vector_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::control_vector_t

input vector type

◆ state_matrix_t

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

typedef Base::state_matrix_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::state_matrix_t

state Jacobian type

◆ state_control_matrix_t

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

typedef Base::state_control_matrix_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::state_control_matrix_t

input Jacobian type

◆ system_t

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

typedef ControlledSystem<STATE_DIM, CONTROL_DIM, SCALAR> ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::system_t

type of system to be linearized

Constructor & Destructor Documentation

◆ SystemLinearizer() [1/2]

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::SystemLinearizer	(	std::shared_ptr< system_t >	nonlinearSystem,
		bool	doubleSidedDerivative = `true`
	)

inline

default constructor

Initializes the linearizer with a non-linear system.

Parameters

nonlinearSystem	non-linear system to linearize
doubleSidedDerivative	if true, double sided numerical differentiation is used

References ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_, ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::isSecondOrderSystem_, and ct::core::SECOND_ORDER.

◆ SystemLinearizer() [2/2]

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::SystemLinearizer ( const SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR > & arg )

inline

copy constructor

◆ ~SystemLinearizer()

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

virtual ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::~SystemLinearizer ( )

inlinevirtual

destructor

Member Function Documentation

◆ clone()

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

SystemLinearizer<STATE_DIM, CONTROL_DIM, SCALAR>* ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::clone ( ) const

inlineoverridevirtual

deep cloning

Implements ct::core::LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >.

Referenced by TEST().

◆ getDerivativeState()

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

virtual const state_matrix_t& ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeState	(	const state_vector_t &	x,
		const control_vector_t &	u,
		const time_t	t = `0.0`
	)

inlineoverridevirtual

get the Jacobian with respect to the state

This computes the linearization of the system with respect to the state at a given point $ x=x_s $ , $ u=u_s $ , i.e. it computes

$A = \frac{df}{dx} |_{x=x_s, u=u_s}$

Parameters

x	state to linearize at
u	control to linearize at
t	time

Returns: Jacobian wrt state

Implements ct::core::LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >.

References ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_, ct::core::DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeState(), ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::isSecondOrderSystem_, ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_, and t.

Referenced by TEST().

◆ getDerivativeControl()

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

virtual const state_control_matrix_t& ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeControl	(	const state_vector_t &	x,
		const control_vector_t &	u,
		const time_t	t = `0.0`
	)

inlineoverridevirtual

get the Jacobian with respect to the input

This computes the linearization of the system with respect to the input at a given point $ x=x_s $ , $ u=u_s $ , i.e. it computes

$B = \frac{df}{du} |_{x=x_s, u=u_s}$

Parameters

x	state to linearize at
u	control to linearize at
t	time

Returns: Jacobian wrt input

Implements ct::core::LinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >.

References ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, ct::core::DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeControl(), ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::isSecondOrderSystem_, ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_, and t.

Referenced by TEST().

Member Data Documentation

◆ Base

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef LinearSystem<STATE_DIM, CONTROL_DIM, SCALAR> ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::Base

Base class type.

◆ nonlinearSystem_

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

std::shared_ptr<system_t> ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::nonlinearSystem_

protected

instance of non-linear system

◆ linearizer_

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

DynamicsLinearizerNumDiff<STATE_DIM, CONTROL_DIM, SCALAR, SCALAR> ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_

protected

instance of numerical-linearizer

Referenced by ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeControl(), and ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeState().

◆ dFdx_

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

state_matrix_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_

protected

Jacobian wrt state.

Referenced by ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeState(), and ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::SystemLinearizer().

◆ dFdu_

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

state_control_matrix_t ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_

protected

Jacobian wrt input.

Referenced by ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeControl(), and ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::SystemLinearizer().

◆ isSecondOrderSystem_

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>

bool ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::isSecondOrderSystem_

protected

flag if system is a second order system

Referenced by ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeControl(), ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeState(), and ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::SystemLinearizer().

The documentation for this class was generated from the following file:

/home/gim2rng/ct_devel_ws/src/control-toolbox/ct_core/include/ct/core/systems/continuous_time/linear/SystemLinearizer.h

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double> class ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >

Member Typedef Documentation

◆ time_t

◆ state_vector_t

◆ control_vector_t

◆ state_matrix_t

◆ state_control_matrix_t

◆ system_t

Constructor & Destructor Documentation

◆ SystemLinearizer() [1/2]

◆ SystemLinearizer() [2/2]

◆ ~SystemLinearizer()

Member Function Documentation

◆ clone()

◆ getDerivativeState()

◆ getDerivativeControl()

Member Data Documentation

◆ Base

◆ nonlinearSystem_

◆ linearizer_

◆ dFdx_

◆ dFdu_

◆ isSecondOrderSystem_

template<size_t STATE_DIM, size_t CONTROL_DIM, typename SCALAR = double>
class ct::core::SystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >