Multiple-shooting C/GMRES solver for nonlinear MPC. More...

#include <multiple_shooting_cgmres_solver.hpp>

Public Types
using	MultipleShootingNLP_ = detail::MultipleShootingNLP< OCP, N >

using	ContinuationGMRES_ = detail::ContinuationGMRESCondensing< MultipleShootingNLP_ >

using	MatrixFreeGMRES_ = detail::MatrixFreeGMRES< ContinuationGMRES_, kmax >

Public Member Functions
	MultipleShootingCGMRESSolver (const OCP &ocp, const Horizon &horizon, const SolverSettings &settings)
	Constructs the multiple-shooting C/GMRES solver. More...

	MultipleShootingCGMRESSolver ()=default
	Default constructor. More...

	~MultipleShootingCGMRESSolver ()=default
	Default destructor. More...

template<typename VectorType >
void	set_u (const MatrixBase< VectorType > &u)
	Sets the control input vector. More...

template<typename VectorType >
void	set_uc (const MatrixBase< VectorType > &uc)
	Sets the control input vector and Lagrange multiplier with respect to the equality constraints. More...

template<typename VectorType >
void	set_x (const MatrixBase< VectorType > &x)
	Sets the state vector. More...

template<typename VectorType >
void	set_lmd (const MatrixBase< VectorType > &lmd)
	Sets the costate vector. More...

template<typename VectorType >
void	set_dummy (const MatrixBase< VectorType > &dummy)
	Sets the dummy input vector with respect to the control input bounds constraint. More...

template<typename VectorType >
void	set_mu (const MatrixBase< VectorType > &mu)
	Sets the Lagrange multiplier with respect to the control input bounds constraint. More...

template<typename T >
void	set_u_array (const T &u_array)
	Sets the array of control input vector. More...

template<typename T >
void	set_uc_array (const T &uc_array)
	Sets the array of control input vector and Lagrange multiplier with respect to the equality constraints. More...

template<typename T >
void	set_x_array (const T &x_array)
	Sets the array of state vector. More...

template<typename T >
void	set_lmd_array (const T &lmd_array)
	Sets the array of costate vector. More...

template<typename T >
void	set_dummy_array (const T &dummy_array)
	Sets the array of the dummy input vector with respect to the control input bounds constraint. More...

template<typename T >
void	set_mu_array (const T &mu_array)
	Sets the array of the Lagrange multiplier with respect to the control input bounds constraint. More...

template<typename VectorType >
void	init_x (const Scalar t, const MatrixBase< VectorType > &x)
	Initializes the state vectors by simulating the system dynamics over the horizon. More...

template<typename VectorType >
void	init_lmd (const Scalar t, const MatrixBase< VectorType > &x)
	Initializes the costate vectors by simulating the system costate dynamics over the horizon. More...

template<typename VectorType >
void	init_x_lmd (const Scalar t, const MatrixBase< VectorType > &x)
	Initializes the state vectors and costate vectors by simulating the system dynamics and system costate dynamcis over the horizon. More...

void	init_dummy_mu ()
	Initializes the dummy input vectors and Lagrange multipliers with respect to the control input bounds constraint. More...

const std::array< Vector< nu >, N > &	uopt () const
	Getter of the optimal solution. More...

const std::array< Vector< nuc >, N > &	ucopt () const
	Getter of the optimal solution. More...

const std::array< Vector< nx >, N+1 > &	xopt () const
	Getter of the optimal solution. More...

const std::array< Vector< nx >, N+1 > &	lmdopt () const
	Getter of the optimal solution. More...

const std::array< Vector< nub >, N > &	dummyopt () const
	Getter of the optimal solution. More...

const std::array< Vector< nub >, N > &	muopt () const
	Getter of the optimal solution. More...

Scalar	optError () const
	Gets the l2-norm of the current optimality errors. More...

template<typename VectorType >
Scalar	optError (const Scalar t, const MatrixBase< VectorType > &x)
	Computes and gets the l2-norm of the current optimality errors. More...

template<typename VectorType >
void	update (const Scalar t, const MatrixBase< VectorType > &x)
	Updates the solution by performing C/GMRES method. More...

TimingProfile	getProfile () const
	Get timing result as TimingProfile. More...

void	disp (std::ostream &os) const

Static Public Attributes
static constexpr int	nx = OCP::nx
	Dimension of the state. More...

static constexpr int	nu = OCP::nu
	Dimension of the control input. More...

static constexpr int	nc = OCP::nc
	Dimension of the equality constraints. More...

static constexpr int	nuc = nu + nc
	Dimension of the concatenation of the control input and equality constraints. More...

static constexpr int	nub = OCP::nub
	Dimension of the bound constraints on the control input. More...

static constexpr int	dim = nuc * N
	Dimension of the linear problem solved by the GMRES solver. More...

Friends
std::ostream &	operator<< (std::ostream &os, const MultipleShootingCGMRESSolver &solver)

Detailed Description

template<class OCP, int N, int kmax>
class cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >

Multiple-shooting C/GMRES solver for nonlinear MPC.

Template Parameters

OCP	A definition of the optimal control problem (OCP).
N	Number of discretizationn grids of the horizon. Must be positive.
kmax	Maximum number of the GMRES iterations. Must be positive.

Member Typedef Documentation

◆ ContinuationGMRES_

template<class OCP , int N, int kmax>

using cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::ContinuationGMRES_ = detail::ContinuationGMRESCondensing<MultipleShootingNLP_>

◆ MatrixFreeGMRES_

template<class OCP , int N, int kmax>

using cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::MatrixFreeGMRES_ = detail::MatrixFreeGMRES<ContinuationGMRES_, kmax>

◆ MultipleShootingNLP_

template<class OCP , int N, int kmax>

using cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::MultipleShootingNLP_ = detail::MultipleShootingNLP<OCP, N>

Constructor & Destructor Documentation

◆ MultipleShootingCGMRESSolver() [1/2]

template<class OCP , int N, int kmax>

cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::MultipleShootingCGMRESSolver	(	const OCP &	ocp,
		const Horizon &	horizon,
		const SolverSettings &	settings
	)

inline

Constructs the multiple-shooting C/GMRES solver.

Parameters

[in]	ocp	A definition of the optimal control problem (OCP).
[in]	horizon	Prediction horizon of MPC.
[in]	settings	Solver settings.

◆ MultipleShootingCGMRESSolver() [2/2]

template<class OCP , int N, int kmax>

cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::MultipleShootingCGMRESSolver ( )

default

Default constructor.

◆ ~MultipleShootingCGMRESSolver()

template<class OCP , int N, int kmax>

cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::~MultipleShootingCGMRESSolver ( )

default

Default destructor.

Member Function Documentation

◆ disp()

template<class OCP , int N, int kmax>

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::disp ( std::ostream & os ) const

inline

◆ dummyopt()

template<class OCP , int N, int kmax>

const std::array< Vector< nub >, N > & cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::dummyopt ( ) const

inline

Getter of the optimal solution.

Returns: const reference to the optimal dummy input vectors with respect to the control input bounds constraint over the horizon.

◆ getProfile()

template<class OCP , int N, int kmax>

TimingProfile cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::getProfile ( ) const

inline

Get timing result as TimingProfile.

Returns: Timing profile.

◆ init_dummy_mu()

template<class OCP , int N, int kmax>

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::init_dummy_mu ( )

inline

Initializes the dummy input vectors and Lagrange multipliers with respect to the control input bounds constraint.

◆ init_lmd()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::init_lmd	(	const Scalar	t,
		const MatrixBase< VectorType > &	x
	)

inline

Initializes the costate vectors by simulating the system costate dynamics over the horizon.

Parameters

[in]	t	Initial time of the horizon.
[in]	x	Initial state of the horizon. Size must be MultipleShootingCGMRESSolver::nx.

◆ init_x()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::init_x	(	const Scalar	t,
		const MatrixBase< VectorType > &	x
	)

inline

Initializes the state vectors by simulating the system dynamics over the horizon.

Parameters

[in]	t	Initial time of the horizon.
[in]	x	Initial state of the horizon. Size must be MultipleShootingCGMRESSolver::nx.

◆ init_x_lmd()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::init_x_lmd	(	const Scalar	t,
		const MatrixBase< VectorType > &	x
	)

inline

Initializes the state vectors and costate vectors by simulating the system dynamics and system costate dynamcis over the horizon.

Parameters

[in]	t	Initial time of the horizon.
[in]	x	Initial state of the horizon. Size must be MultipleShootingCGMRESSolver::nx.

◆ lmdopt()

template<class OCP , int N, int kmax>

const std::array< Vector< nx >, N+1 > & cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::lmdopt ( ) const

inline

Getter of the optimal solution.

Returns: const reference to the optimal costate vectors over the horizon.

◆ muopt()

template<class OCP , int N, int kmax>

const std::array< Vector< nub >, N > & cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::muopt ( ) const

inline

Getter of the optimal solution.

Returns: const reference to the Lagrange multipliers with respect to the control input bounds constraint over the horizon.

◆ optError() [1/2]

template<class OCP , int N, int kmax>

Scalar cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::optError ( ) const

inline

Gets the l2-norm of the current optimality errors.

Returns: The l2-norm of the current optimality errors.

◆ optError() [2/2]

template<class OCP , int N, int kmax>

template<typename VectorType >

Scalar cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::optError	(	const Scalar	t,
		const MatrixBase< VectorType > &	x
	)

inline

Computes and gets the l2-norm of the current optimality errors.

Parameters

[in]	t	Initial time of the horizon.
[in]	x	Initial state of the horizon. Size must be MultipleShootingCGMRESSolver::nx.

Returns: The l2-norm of the current optimality errors.

◆ set_dummy()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_dummy ( const MatrixBase< VectorType > & dummy )

inline

Sets the dummy input vector with respect to the control input bounds constraint.

Parameters

[in] dummy The dummy input vector. Size must be MultipleShootingCGMRESSolver::nub.

◆ set_dummy_array()

template<class OCP , int N, int kmax>

template<typename T >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_dummy_array ( const T & dummy_array )

inline

Sets the array of the dummy input vector with respect to the control input bounds constraint.

Parameters

[in] dummy_array A container (std::vector, std::array, etc.) of the dummy input vector. Size must be N and size of each element must be MultipleShootingCGMRESSolver::nub.

◆ set_lmd()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_lmd ( const MatrixBase< VectorType > & lmd )

inline

Sets the costate vector.

Parameters

[in] lmd The costate vector. Size must be MultipleShootingCGMRESSolver::nx.

◆ set_lmd_array()

template<class OCP , int N, int kmax>

template<typename T >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_lmd_array ( const T & lmd_array )

inline

Sets the array of costate vector.

Parameters

[in] lmd_array A container (std::vector, std::array, etc.) of the costate vector. Size must be N+1 and size of each element must be MultipleShootingCGMRESSolver::nx.

◆ set_mu()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_mu ( const MatrixBase< VectorType > & mu )

inline

Sets the Lagrange multiplier with respect to the control input bounds constraint.

Parameters

[in] mu The Lagrange multiplier. Size must be MultipleShootingCGMRESSolver::nub.

◆ set_mu_array()

template<class OCP , int N, int kmax>

template<typename T >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_mu_array ( const T & mu_array )

inline

Sets the array of the Lagrange multiplier with respect to the control input bounds constraint.

Parameters

[in] mu_array A container (std::vector, std::array, etc.) of the Lagrange multiplier. Size must be N and size of each element must be MultipleShootingCGMRESSolver::nub.

◆ set_u()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_u ( const MatrixBase< VectorType > & u )

inline

Sets the control input vector.

Parameters

[in] u The control input vector. Size must be MultipleShootingCGMRESSolver::nu.

◆ set_u_array()

template<class OCP , int N, int kmax>

template<typename T >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_u_array ( const T & u_array )

inline

Sets the array of control input vector.

Parameters

[in] u_array A container (std::vector, std::array, etc.) of the control input vector. Size must be N and size of each element must be MultipleShootingCGMRESSolver::nu.

◆ set_uc()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_uc ( const MatrixBase< VectorType > & uc )

inline

Sets the control input vector and Lagrange multiplier with respect to the equality constraints.

Parameters

[in] uc Concatenatin of the control input vector and Lagrange multiplier with respect to the equality constraints. Size must be MultipleShootingCGMRESSolver::nuc.

◆ set_uc_array()

template<class OCP , int N, int kmax>

template<typename T >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_uc_array ( const T & uc_array )

inline

Sets the array of control input vector and Lagrange multiplier with respect to the equality constraints.

Parameters

[in] uc_array A container (std::vector, std::array, etc.) of the concatenatin of the control input vector and Lagrange multiplier with respect to the equality constraints. Size must be N and size of each element must be MultipleShootingCGMRESSolver::nuc.

◆ set_x()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_x ( const MatrixBase< VectorType > & x )

inline

Sets the state vector.

Parameters

[in] x The state vector. Size must be MultipleShootingCGMRESSolver::nx.

◆ set_x_array()

template<class OCP , int N, int kmax>

template<typename T >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::set_x_array ( const T & x_array )

inline

Sets the array of state vector.

Parameters

[in] x_array A container (std::vector, std::array, etc.) of the state vector. Size must be N+1 and size of each element must be MultipleShootingCGMRESSolver::nx.

◆ ucopt()

template<class OCP , int N, int kmax>

const std::array< Vector< nuc >, N > & cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::ucopt ( ) const

inline

Getter of the optimal solution.

Returns: const reference to the optimal concatenatins of the control input vector and Lagrange multiplier with respect to the equality constraints.

◆ uopt()

template<class OCP , int N, int kmax>

const std::array< Vector< nu >, N > & cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::uopt ( ) const

inline

Getter of the optimal solution.

Returns: const reference to the optimal control input vectors over the horizon.

◆ update()

template<class OCP , int N, int kmax>

template<typename VectorType >

void cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::update	(	const Scalar	t,
		const MatrixBase< VectorType > &	x
	)

inline

Updates the solution by performing C/GMRES method.

Parameters

[in]	t	Initial time of the horizon.
[in]	x	Initial state of the horizon. Size must be MultipleShootingCGMRESSolver::nx.

◆ xopt()

template<class OCP , int N, int kmax>

const std::array< Vector< nx >, N+1 > & cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::xopt ( ) const

inline

Getter of the optimal solution.

Returns: const reference to the optimal state vectors over the horizon.

Friends And Related Function Documentation

◆ operator<<

template<class OCP , int N, int kmax>

std::ostream & operator<<	(	std::ostream &	os,
		const MultipleShootingCGMRESSolver< OCP, N, kmax > &	solver
	)

friend

Member Data Documentation

◆ dim

template<class OCP , int N, int kmax>

constexpr int cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::dim = nuc * N

staticconstexpr

Dimension of the linear problem solved by the GMRES solver.

◆ nc

template<class OCP , int N, int kmax>

constexpr int cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::nc = OCP::nc

staticconstexpr

Dimension of the equality constraints.

◆ nu

template<class OCP , int N, int kmax>

constexpr int cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::nu = OCP::nu

staticconstexpr

Dimension of the control input.

◆ nub

template<class OCP , int N, int kmax>

constexpr int cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::nub = OCP::nub

staticconstexpr

Dimension of the bound constraints on the control input.

◆ nuc

template<class OCP , int N, int kmax>

constexpr int cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::nuc = nu + nc

staticconstexpr

Dimension of the concatenation of the control input and equality constraints.

◆ nx

template<class OCP , int N, int kmax>

constexpr int cgmres::MultipleShootingCGMRESSolver< OCP, N, kmax >::nx = OCP::nx

staticconstexpr

Dimension of the state.

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

/github/workspace/include/cgmres/multiple_shooting_cgmres_solver.hpp

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ ContinuationGMRES_

◆ MatrixFreeGMRES_

◆ MultipleShootingNLP_

Constructor & Destructor Documentation

◆ MultipleShootingCGMRESSolver() [1/2]

◆ MultipleShootingCGMRESSolver() [2/2]

◆ ~MultipleShootingCGMRESSolver()

Member Function Documentation

◆ disp()

◆ dummyopt()

◆ getProfile()

◆ init_dummy_mu()

◆ init_lmd()

◆ init_x()

◆ init_x_lmd()

◆ lmdopt()

◆ muopt()

◆ optError() [1/2]

◆ optError() [2/2]

◆ set_dummy()

◆ set_dummy_array()

◆ set_lmd()

◆ set_lmd_array()

◆ set_mu()

◆ set_mu_array()

◆ set_u()

◆ set_u_array()

◆ set_uc()

◆ set_uc_array()

◆ set_x()

◆ set_x_array()

◆ ucopt()

◆ uopt()

◆ update()

◆ xopt()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ dim

◆ nc

◆ nu

◆ nub

◆ nuc

◆ nx