Definition of the optimal control problem (OCP) of cartpole. More...

#include <ocp.hpp>

Public Member Functions
void	disp (std::ostream &os) const

void	synchronize ()
	Synchrozies the internal parameters of this OCP with the external references. This method is called at the beginning of each MPC update. More...

void	eval_f (const double t, const double x, const double u, double *dx) const
	Computes the state equation dx = f(t, x, u). More...

void	eval_phix (const double t, const double x, double phix) const
	Computes the partial derivative of terminal cost with respect to state, i.e., phix = dphi/dx(t, x). More...

void	eval_hx (const double t, const double x, const double u, const double lmd, double hx) const
	Computes the partial derivative of the Hamiltonian with respect to state, i.e., hx = dH/dx(t, x, u, lmd). More...

void	eval_hu (const double t, const double x, const double u, const double lmd, double hu) const
	Computes the partial derivative of the Hamiltonian with respect to control input and the equality constraints, i.e., hu = dH/du(t, x, u, lmd). More...

template<typename VectorType1 , typename VectorType2 , typename VectorType3 >
void	eval_f (const double t, const MatrixBase< VectorType1 > &x, const MatrixBase< VectorType2 > &u, const MatrixBase< VectorType3 > &dx) const
	Computes the state equation dx = f(t, x, u). More...

template<typename VectorType1 , typename VectorType2 >
void	eval_phix (const double t, const MatrixBase< VectorType1 > &x, const MatrixBase< VectorType2 > &phix) const
	Computes the partial derivative of terminal cost with respect to state, i.e., phix = dphi/dx(t, x). More...

template<typename VectorType1 , typename VectorType2 , typename VectorType3 , typename VectorType4 >
void	eval_hx (const double t, const MatrixBase< VectorType1 > &x, const MatrixBase< VectorType2 > &uc, const MatrixBase< VectorType3 > &lmd, const MatrixBase< VectorType4 > &hx) const
	Computes the partial derivative of the Hamiltonian with respect to the state, i.e., hx = dH/dx(t, x, u, lmd). More...

template<typename VectorType1 , typename VectorType2 , typename VectorType3 , typename VectorType4 >
void	eval_hu (const double t, const MatrixBase< VectorType1 > &x, const MatrixBase< VectorType2 > &uc, const MatrixBase< VectorType3 > &lmd, const MatrixBase< VectorType4 > &hu) const
	Computes the partial derivative of the Hamiltonian with respect to control input and the equality constraints, i.e., hu = dH/du(t, x, u, lmd). More...

Public Attributes
double	m_c = 2

double	m_p = 0.2

double	l = 0.5

double	g = 9.80665

std::array< double, 4 >	q = {2.5, 10, 0.01, 0.01}

std::array< double, 4 >	q_terminal = {2.5, 10, 0.01, 0.01}

std::array< double, 4 >	x_ref = {0, M_PI, 0, 0}

std::array< double, 1 >	r = {1}

std::array< double, nub >	umin = {-15.0}

std::array< double, nub >	umax = {15.0}

std::array< double, nub >	dummy_weight = {0.1}

Static Public Attributes
static constexpr int	nx = 4
	Dimension of the state. More...

static constexpr int	nu = 1
	Dimension of the control input. More...

static constexpr int	nc = 0
	Dimension of the equality constraints. More...

static constexpr int	nh = 0
	Dimension of the Fischer-Burmeister function (already counded in nc). More...

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

static constexpr int	nub = 1
	Dimension of the bound constraints on the control input. More...

static constexpr std::array< int, nub >	ubound_indices = {0}

Friends
std::ostream &	operator<< (std::ostream &os, const OCP_cartpole &ocp)

Detailed Description

Definition of the optimal control problem (OCP) of cartpole.

Member Function Documentation

◆ disp()

void cgmres::OCP_cartpole::disp ( std::ostream & os ) const

inline

◆ eval_f() [1/2]

void cgmres::OCP_cartpole::eval_f	(	const double	t,
		const double *	x,
		const double *	u,
		double *	dx
	)		const

inline

Computes the state equation dx = f(t, x, u).

Parameters

[in]	t	Time.
[in]	x	State.
[in]	u	Control input.
[out]	dx	Evaluated value of the state equation.

Remarks: This method is intended to be used inside of the cgmres solvers and does not check size of each argument. Use the overloaded method if you call this outside of the cgmres solvers.

◆ eval_f() [2/2]

template<typename VectorType1 , typename VectorType2 , typename VectorType3 >

void cgmres::OCP_cartpole::eval_f	(	const double	t,
		const MatrixBase< VectorType1 > &	x,
		const MatrixBase< VectorType2 > &	u,
		const MatrixBase< VectorType3 > &	dx
	)		const

inline

Computes the state equation dx = f(t, x, u).

Parameters

[in]	t	Time.
[in]	x	State. Size must be nx.
[in]	u	Control input. Size must be nu.
[out]	dx	Evaluated value of the state equation. Size must be nx.

◆ eval_hu() [1/2]

void cgmres::OCP_cartpole::eval_hu	(	const double	t,
		const double *	x,
		const double *	u,
		const double *	lmd,
		double *	hu
	)		const

inline

Computes the partial derivative of the Hamiltonian with respect to control input and the equality constraints, i.e., hu = dH/du(t, x, u, lmd).

Parameters

[in]	t	Time.
[in]	x	State.
[in]	u	Concatenatin of the control input and Lagrange multiplier with respect to the equality constraints.
[in]	lmd	Costate.
[out]	hu	Evaluated value of the partial derivative of the Hamiltonian.

Remarks: This method is intended to be used inside of the cgmres solvers and does not check size of each argument. Use the overloaded method if you call this outside of the cgmres solvers.

◆ eval_hu() [2/2]

template<typename VectorType1 , typename VectorType2 , typename VectorType3 , typename VectorType4 >

void cgmres::OCP_cartpole::eval_hu	(	const double	t,
		const MatrixBase< VectorType1 > &	x,
		const MatrixBase< VectorType2 > &	uc,
		const MatrixBase< VectorType3 > &	lmd,
		const MatrixBase< VectorType4 > &	hu
	)		const

inline

Computes the partial derivative of the Hamiltonian with respect to control input and the equality constraints, i.e., hu = dH/du(t, x, u, lmd).

Parameters

[in]	t	Time.
[in]	x	State. Size must be nx.
[in]	uc	Concatenatin of the control input and Lagrange multiplier with respect to the equality constraints. Size must be nuc.
[in]	lmd	Costate. Size must be nx.
[out]	hu	Evaluated value of the partial derivative of the Hamiltonian. Size must be nuc.

◆ eval_hx() [1/2]

void cgmres::OCP_cartpole::eval_hx	(	const double	t,
		const double *	x,
		const double *	u,
		const double *	lmd,
		double *	hx
	)		const

inline

Computes the partial derivative of the Hamiltonian with respect to state, i.e., hx = dH/dx(t, x, u, lmd).

Parameters

[in]	t	Time.
[in]	x	State.
[in]	u	Concatenatin of the control input and Lagrange multiplier with respect to the equality constraints.
[in]	lmd	Costate.
[out]	hx	Evaluated value of the partial derivative of the Hamiltonian.

Remarks: This method is intended to be used inside of the cgmres solvers and does not check size of each argument. Use the overloaded method if you call this outside of the cgmres solvers.

◆ eval_hx() [2/2]

template<typename VectorType1 , typename VectorType2 , typename VectorType3 , typename VectorType4 >

void cgmres::OCP_cartpole::eval_hx	(	const double	t,
		const MatrixBase< VectorType1 > &	x,
		const MatrixBase< VectorType2 > &	uc,
		const MatrixBase< VectorType3 > &	lmd,
		const MatrixBase< VectorType4 > &	hx
	)		const

inline

Computes the partial derivative of the Hamiltonian with respect to the state, i.e., hx = dH/dx(t, x, u, lmd).

Parameters

[in]	t	Time.
[in]	x	State. Size must be nx.
[in]	uc	Concatenatin of the control input and Lagrange multiplier with respect to the equality constraints. Size must be nuc.
[in]	lmd	Costate. Size must be nx.
[out]	hx	Evaluated value of the partial derivative of the Hamiltonian. Size must be nx.

◆ eval_phix() [1/2]

void cgmres::OCP_cartpole::eval_phix	(	const double	t,
		const double *	x,
		double *	phix
	)		const

inline

Computes the partial derivative of terminal cost with respect to state, i.e., phix = dphi/dx(t, x).

Parameters

[in]	t	Time.
[in]	x	State.
[out]	phix	Evaluated value of the partial derivative of terminal cost.

Remarks: This method is intended to be used inside of the cgmres solvers and does not check size of each argument. Use the overloaded method if you call this outside of the cgmres solvers.

◆ eval_phix() [2/2]

template<typename VectorType1 , typename VectorType2 >

void cgmres::OCP_cartpole::eval_phix	(	const double	t,
		const MatrixBase< VectorType1 > &	x,
		const MatrixBase< VectorType2 > &	phix
	)		const

inline

Computes the partial derivative of terminal cost with respect to state, i.e., phix = dphi/dx(t, x).

Parameters

[in]	t	Time.
[in]	x	State. Size must be nx.
[out]	phix	Evaluated value of the partial derivative of terminal cost. Size must be nx.

◆ synchronize()

void cgmres::OCP_cartpole::synchronize ( )

inline

Synchrozies the internal parameters of this OCP with the external references. This method is called at the beginning of each MPC update.

Friends And Related Function Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	os,
		const OCP_cartpole &	ocp
	)

friend

Member Data Documentation

◆ dummy_weight

std::array<double, nub> cgmres::OCP_cartpole::dummy_weight = {0.1}

◆ g

double cgmres::OCP_cartpole::g = 9.80665

◆ l

double cgmres::OCP_cartpole::l = 0.5

◆ m_c

double cgmres::OCP_cartpole::m_c = 2

◆ m_p

double cgmres::OCP_cartpole::m_p = 0.2

◆ nc

constexpr int cgmres::OCP_cartpole::nc = 0

staticconstexpr

Dimension of the equality constraints.

◆ nh

constexpr int cgmres::OCP_cartpole::nh = 0

staticconstexpr

Dimension of the Fischer-Burmeister function (already counded in nc).

◆ nu

constexpr int cgmres::OCP_cartpole::nu = 1

staticconstexpr

Dimension of the control input.

◆ nub

constexpr int cgmres::OCP_cartpole::nub = 1

staticconstexpr

Dimension of the bound constraints on the control input.

◆ nuc

constexpr int cgmres::OCP_cartpole::nuc = nu + nc

staticconstexpr

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

◆ nx

constexpr int cgmres::OCP_cartpole::nx = 4

staticconstexpr

Dimension of the state.

◆ q

std::array<double, 4> cgmres::OCP_cartpole::q = {2.5, 10, 0.01, 0.01}

◆ q_terminal

std::array<double, 4> cgmres::OCP_cartpole::q_terminal = {2.5, 10, 0.01, 0.01}

◆ r

std::array<double, 1> cgmres::OCP_cartpole::r = {1}

◆ ubound_indices

constexpr std::array<int, nub> cgmres::OCP_cartpole::ubound_indices = {0}

staticconstexpr

◆ umax

std::array<double, nub> cgmres::OCP_cartpole::umax = {15.0}

◆ umin

std::array<double, nub> cgmres::OCP_cartpole::umin = {-15.0}

◆ x_ref

std::array<double, 4> cgmres::OCP_cartpole::x_ref = {0, M_PI, 0, 0}

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

/github/workspace/examples/cpp/cartpole/ocp.hpp

Public Member Functions

Public Attributes

Static Public Attributes

Friends

Detailed Description

Member Function Documentation

◆ disp()

◆ eval_f() [1/2]

◆ eval_f() [2/2]

◆ eval_hu() [1/2]

◆ eval_hu() [2/2]

◆ eval_hx() [1/2]

◆ eval_hx() [2/2]

◆ eval_phix() [1/2]

◆ eval_phix() [2/2]

◆ synchronize()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ dummy_weight

◆ g

◆ l

◆ m_c

◆ m_p

◆ nc

◆ nh

◆ nu

◆ nub

◆ nuc

◆ nx

◆ q

◆ q_terminal

◆ r

◆ ubound_indices

◆ umax

◆ umin

◆ x_ref