Computes the linearization of a general non-linear DiscreteControlledSystem using Automatic Differentiation (without code generation) More...

#include <DiscreteSystemLinearizerAD.h>

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

Public Types
typedef CppAD::AD< SCALAR >	ADScalar

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

typedef DynamicsLinearizerAD< STATE_DIM, CONTROL_DIM, ADScalar, int >	linearizer_t
	type of linearizer to be used 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
	DiscreteSystemLinearizerAD (std::shared_ptr< system_t > nonlinearSystem)
	control Jacobian type (B) More...

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

virtual	~DiscreteSystemLinearizerAD ()
	destructor More...

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

const state_matrix_t &	getDerivativeState (const state_vector_t &x, const control_vector_t &u, const int t=0)
	get the Jacobian with respect to the state More...

const state_control_matrix_t &	getDerivativeControl (const state_vector_t &x, const control_vector_t &u, const int t=0)
	get the Jacobian with respect to the input More...

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
state_matrix_t	dFdx_

state_control_matrix_t	dFdu_

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

linearizer_t	linearizer_
	instance of ad-linearizer 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::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >

Computes the linearization of a general non-linear DiscreteControlledSystem using Automatic Differentiation (without code generation)

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

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

Note: This is generally the most accurate way to generate the linearization of system dynamics together with DiscreteSystemLinearizerADCG. However, the latter is much faster. Consider using the latter for production code.

Unit test AutoDiffLinearizerTest.cpp illustrates the use of this class.

Warning: You should ensure that your DiscreteControlledSystem is templated on the scalar type and does not contain branching (if/else statements, switch cases etc.); This function still has some issues with pure time dependency

Todo:: Make time an Auto-Diff parameter

Template Parameters

STATE_DIM	dimension of state vector
CONTROL_DIM	dimension of control vector
SCALAR	primitive type of resultant linear system

Examples:: AutoDiffLinearizerTest.cpp.

Member Typedef Documentation

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

typedef CppAD::AD<SCALAR> ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::ADScalar

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

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

type of system to be linearized

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

typedef DynamicsLinearizerAD<STATE_DIM, CONTROL_DIM, ADScalar, int> ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_t

type of linearizer to be used

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

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

state vector type

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

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

control vector type

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

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

state Jacobian type (A)

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

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

Constructor & Destructor Documentation

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

ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::DiscreteSystemLinearizerAD ( std::shared_ptr< system_t > nonlinearSystem )

inline

control Jacobian type (B)

default constructor

Parameters

nonlinearSystem non-linear system instance to linearize

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

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

inline

copy constructor

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

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

inlinevirtual

destructor

Member Function Documentation

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

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

inlineoverridevirtual

deep cloning

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

Referenced by TEST().

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

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

inline

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

References ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_, ct::core::DynamicsLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeState(), ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_, and t.

Referenced by TEST().

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

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

inline

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

References ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, ct::core::DynamicsLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeControl(), ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_, and t.

Referenced by TEST().

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

void ct::core::DiscreteSystemLinearizerAD< 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::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::dFdu_, ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::dFdx_, ct::core::DynamicsLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeControl(), ct::core::DynamicsLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR, TIME >::getDerivativeState(), and ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_.

Member Data Documentation

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::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::Base

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

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

protected

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

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

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

protected

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

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

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

protected

instance of non-linear system

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

linearizer_t ct::core::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >::linearizer_

protected

instance of ad-linearizer

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

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

/home/adrl/code/src/control-toolbox/ct_core/include/ct/core/systems/discrete_time/linear/DiscreteSystemLinearizerAD.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::DiscreteSystemLinearizerAD< STATE_DIM, CONTROL_DIM, SCALAR >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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