Computes the linearization of a general non-linear ControlledSystem using Automatic Differentiation with code generation. More...

#include <ADCodegenLinearizer.h>

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

Public Types
typedef CppAD::AD< CppAD::cg::CG< SCALAR > >	ADCGScalar
	Autodiff codegen type. More...

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

typedef DynamicsLinearizerADCG< STATE_DIM, CONTROL_DIM, ADCGScalar, ADCGScalar >	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
	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...

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
	ADCodegenLinearizer (std::shared_ptr< system_t > nonlinearSystem, bool cacheJac=true)
	default constructor More...

	ADCodegenLinearizer (const ADCodegenLinearizer< STATE_DIM, CONTROL_DIM > &arg)
	copy constructor More...

ADCodegenLinearizer< 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 SCALAR t=SCALAR(0.0)) override
	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 SCALAR t=SCALAR(0.0)) override
	get the Jacobian with respect to the input More...

void	compileJIT (const std::string &libName="ADCodegenLinearizer")
	compile just-in-time More...

void	generateCode (const std::string &systemName, const std::string &outputDir=ct::core::CODEGEN_OUTPUT_DIR, const std::string &templateDir=ct::core::CODEGEN_TEMPLATE_DIR, const std::string &ns1="core", const std::string &ns2="generated", bool useReverse=false, bool ignoreZero=true)
	generates source code and saves it to file More...

const linearizer_t &	getLinearizer () const
	accessor to the linearizer, e.g. for testing 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 const state_matrix_t &	getDerivativeState (const state_vector_t &x, const control_vector_t &u, const time_t t=time_t(0.0))=0
	get the A matrix of a linear system More...

virtual const state_control_matrix_t &	getDerivativeControl (const state_vector_t &x, const control_vector_t &u, const time_t t=time_t(0.0))=0
	get the B matrix of a linear system 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...

Additional Inherited Members
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::ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >

Computes the linearization of a general non-linear ControlledSystem using Automatic Differentiation with code generation.

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

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

Note: This is generally the most efficient and most accurate way to generate the linearization of system dynamics.

Warning: You should ensure that your ControlledSystem is templated on the scalar type and does not contain branching (if/else statements, switch cases etc.)

The linearization is computed using Auto Differentiation which is then used by a code generator framework to generate efficient code. For convenience just-in-time compilation is provided. However, you can also generate source code directly.

Unit test CodegenTests.cpp illustrates the use of the ADCodeGenLinearizer.

Warning: Depending on the complexity of your system, just-in-time compilation (compileJIT()) can be slow. In that case generate a source code file

Template Parameters

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

Member Typedef Documentation

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

typedef CppAD::AD<CppAD::cg::CG<SCALAR> > ct::core::ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::ADCGScalar

Autodiff codegen type.

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

typedef ControlledSystem<STATE_DIM, CONTROL_DIM, ADCGScalar> ct::core::ADCodegenLinearizer< 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 DynamicsLinearizerADCG<STATE_DIM, CONTROL_DIM, ADCGScalar, ADCGScalar> ct::core::ADCodegenLinearizer< 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::ADCodegenLinearizer< 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::ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::control_vector_t

input vector type

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

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

state Jacobian type

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

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

input Jacobian type

Constructor & Destructor Documentation

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

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

inline

default constructor

Initializes an Auto-Diff codegen linearizer with a ControlledSystem

Parameters

nonlinearSystem	non-linear system instance
cacheJac	if true, caches the Jacobians to prevent recomputation for the same state/input

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

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

inline

copy constructor

Member Function Documentation

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

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

inlineoverridevirtual

deep cloning

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

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

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

inlineoverride

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

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

Warning: Call compileJIT() before calling this function.

Parameters

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

Returns: Jacobian wrt state

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

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

inlineoverride

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

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

Warning: Call compileJIT() before calling this function.

Parameters

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

Returns: Jacobian wrt input

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

void ct::core::ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::compileJIT ( const std::string & libName = "ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >" )

inline

compile just-in-time

Generates the source code, compiles it and dynamically loads the resulting library.

Note: If this function takes a long time, consider generating the source code using generateCode() and compile it before runtime.

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

void ct::core::ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::generateCode	(	const std::string &	systemName,
		const std::string &	outputDir = `ct::core::CODEGEN_OUTPUT_DIR`,
		const std::string &	templateDir = `ct::core::CODEGEN_TEMPLATE_DIR`,
		const std::string &	ns1 = `"core"`,
		const std::string &	ns2 = `"generated"`,
		bool	useReverse = `false`,
		bool	ignoreZero = `true`
	)

inline

generates source code and saves it to file

This generates source code for computing the system linearization and saves it to file. This function uses a template file in which it replaces two placeholders, each identified as the string "AUTOGENERATED_CODE_PLACEHOLDER"

Parameters

systemName	name of the resulting LinearSystem class
outputDir	output directory
templateDir	directory of the template file
ns1	first layer namespace
ns2	second layer namespace
useReverse	if true, uses Auto-Diff reverse mode
ignoreZero	if true, zero entries are not assigned zero

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

const linearizer_t& ct::core::ADCodegenLinearizer< STATE_DIM, CONTROL_DIM, SCALAR >::getLinearizer ( ) const

inline

accessor to the linearizer, e.g. for testing

Member Data Documentation

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

Base class type.

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

/home/adrl/code/src/control-toolbox/ct_core/include/ct/core/systems/continuous_time/linear/ADCodegenLinearizer.h

Public Types

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

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