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

#include <DiscreteSystemLinearizer.h>

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

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

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

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

typedef Base::state_matrix_t	state_matrix_t
	state Jacobian type (A) More...

typedef Base::state_control_matrix_t	state_control_matrix_t

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

typedef Base::state_vector_t	state_vector_t

typedef Base::control_vector_t	control_vector_t

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::DiscreteControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >
typedef DiscreteSystem< STATE_DIM, CONTROL_DIM, SCALAR >	Base

typedef Base::state_vector_t	state_vector_t

typedef Base::control_vector_t	control_vector_t

typedef Base::time_t	time_t

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

typedef StateVector< STATE_DIM, SCALAR >	state_vector_t

typedef ControlVector< CONTROL_DIM, SCALAR >	control_vector_t

Public Member Functions
	DiscreteSystemLinearizer (std::shared_ptr< system_t > nonlinearSystem, bool doubleSidedDerivative=true)
	control Jacobian type (B) More...

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

virtual	~DiscreteSystemLinearizer ()
	destructor More...

DiscreteSystemLinearizer< 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 int n=0)
	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 int n=0)
	get the Jacobian with respect to the input More...

virtual void	getAandB (const state_vector_t &x, const control_vector_t &u, const state_vector_t &x_next, const int n, size_t numSteps, state_matrix_t &A, state_control_matrix_t &B) override
	retrieve discrete-time linear system matrices A and B. More...

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

virtual	~DiscreteLinearSystem ()
	destructor More...

virtual void	propagateControlledDynamics (const state_vector_t &state, const time_t n, const control_vector_t &control, state_vector_t &stateNext) override
	compute the system dynamics More...

void	getAandB (const state_vector_t &x, const control_vector_t &u, const int n, state_matrix_t &A, state_control_matrix_t &B)

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

	DiscreteControlledSystem (std::shared_ptr< DiscreteController< STATE_DIM, CONTROL_DIM, SCALAR >> controller, const SYSTEM_TYPE &type=SYSTEM_TYPE::GENERAL)
	constructor More...

	DiscreteControlledSystem (const ControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR > &arg)
	copy constructor More...

virtual	~DiscreteControlledSystem ()=default
	destructor More...

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

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

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

virtual void	propagateDynamics (const state_vector_t &state, const time_t n, state_vector_t &stateNext) override
	propagates the system dynamics forward by one step More...

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

virtual	~DiscreteSystem ()
	desctructor More...

virtual void	propagateDynamics (const StateVector< STATE_DIM, SCALAR > &state, const time_t n, StateVector< STATE_DIM, SCALAR > &stateNext)=0
	propagates the system dynamics forward by one step More...

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

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef DiscreteLinearSystem< STATE_DIM, CONTROL_DIM, SCALAR >	Base

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

Public Attributes inherited from ct::core::DiscreteControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef std::shared_ptr< DiscreteControlledSystem< STATE_DIM, CONTROL_DIM, SCALAR > >	Ptr

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

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

state_matrix_t	dFdx_
	Jacobian wrt state. More...

state_control_matrix_t	dFdu_
	Jacobian wrt input. More...

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

Protected Attributes inherited from ct::core::DiscreteSystem< STATE_DIM, CONTROL_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::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >

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

This class takes a non-linear DiscreteControlledSystem $ x[n+1] = f(x[n],u[n],n) $ and computes the linearization around a certain point $ x = x_s $ , $ u = u_s $ .

$x[n+1] = A x[n] + B u[n]$

where

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

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 DiscreteSystemLinearizerAD for highest efficiency and accuracy.

Template Parameters

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

Examples:: AutoDiffLinearizerTest.cpp.

Member Typedef Documentation

◆ system_t

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

typedef DiscreteControlledSystem<STATE_DIM, CONTROL_DIM, SCALAR> ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::system_t

type of system to be linearized

◆ state_vector_t

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

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

control vector type

◆ state_matrix_t

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

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

state Jacobian type (A)

◆ state_control_matrix_t

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

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

Constructor & Destructor Documentation

◆ DiscreteSystemLinearizer() [1/2]

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

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

inline

control Jacobian type (B)

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::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, and ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_.

◆ DiscreteSystemLinearizer() [2/2]

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

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

inline

copy constructor

◆ ~DiscreteSystemLinearizer()

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

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

inlinevirtual

destructor

Member Function Documentation

◆ clone()

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

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

inlineoverridevirtual

deep cloning

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

◆ getDerivativeState()

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

virtual const state_matrix_t& ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeState	(	const state_vector_t &	x,
		const control_vector_t &	u,
		const int	n = `0`
	)

inlinevirtual

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
n	index

Returns: Jacobian wrt state

References ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_, ct::core::DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeState(), ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_, and n.

Referenced by TEST().

◆ getDerivativeControl()

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

virtual const state_control_matrix_t& ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getDerivativeControl	(	const state_vector_t &	x,
		const control_vector_t &	u,
		const int	n = `0`
	)

inlinevirtual

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
n	index

Returns: Jacobian wrt input

References ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, ct::core::DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeControl(), ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_, and n.

Referenced by TEST().

◆ getAandB()

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

virtual void ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getAandB	(	const state_vector_t &	x,
		const control_vector_t &	u,
		const state_vector_t &	x_next,
		const int	n,
		size_t	numSteps,
		state_matrix_t &	A,
		state_control_matrix_t &	B
	)

inlineoverridevirtual

retrieve discrete-time linear system matrices A and B.

This computes matrices A and B such that

$x_{n+1} = Ax_n + Bu_n$

Note that the inputs x_next and subSteps are being ignored

Parameters

x	the state setpoint at n
u	the control setpoint at n
n	the time setpoint
x_next	-> ignored
subSteps	-> ignored
A	the resulting linear system matrix A
B	the resulting linear system matrix B

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

References ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_, ct::core::DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeControl(), ct::core::DynamicsLinearizerNumDiff< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeState(), and ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_.

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 DiscreteLinearSystem<STATE_DIM, CONTROL_DIM, SCALAR> ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::Base

◆ nonlinearSystem_

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

std::shared_ptr<system_t> ct::core::DiscreteSystemLinearizer< 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, int> ct::core::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_

protected

instance of numerical-linearizer

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

◆ dFdx_

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

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

protected

Jacobian wrt state.

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

◆ dFdu_

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

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

protected

Jacobian wrt input.

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

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/discrete_time/linear/DiscreteSystemLinearizer.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::DiscreteSystemLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >

Member Typedef Documentation

◆ system_t

◆ state_vector_t

◆ control_vector_t

◆ state_matrix_t

◆ state_control_matrix_t

Constructor & Destructor Documentation

◆ DiscreteSystemLinearizer() [1/2]

◆ DiscreteSystemLinearizer() [2/2]

◆ ~DiscreteSystemLinearizer()

Member Function Documentation

◆ clone()

◆ getDerivativeState()

◆ getDerivativeControl()

◆ getAandB()

Member Data Documentation

◆ Base

◆ nonlinearSystem_

◆ linearizer_

◆ dFdx_

◆ dFdu_

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