Sequential extension for time-invariant system. More...

#include <InvariantSequentialExtension.h>

Public Types
using	_StateSpaceModel = StateSpaceModel< StateDim, InputDim, OutputDim >
	Type of state-space model with fixed dimensions of state, input, and output. More...

Public Member Functions
EIGEN_MAKE_ALIGNED_OPERATOR_NEW	InvariantSequentialExtension (const std::shared_ptr< _StateSpaceModel > &model, int seq_len, bool extend_for_output=false)
	Constructor. More...

int	totalStateDim () const
	Get total state dimension. More...

int	totalInputDim () const
	Get total input dimension. More...

int	totalOutputDim () const
	Get total output dimension. More...

Public Attributes
std::shared_ptr< _StateSpaceModel >	model_
	State-space model. More...

int	seq_len_ = 0
	Sequence length. More...

Eigen::Matrix< double, Eigen::Dynamic, StateDim >	A_seq_
	Sequential extension matrix \(\boldsymbol{\hat{A}}\). More...

Eigen::MatrixXd	B_seq_
	Sequential extension matrix \(\boldsymbol{\hat{B}}\). More...

Eigen::VectorXd	E_seq_
	Sequential extension vector (i.e., offset vector) \(\boldsymbol{\hat{e}}\). More...

Protected Member Functions
void	setup (bool extend_for_output)
	Setup coefficients. More...

Detailed Description

template<int StateDim, int InputDim, int OutputDim>
class CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >

Sequential extension for time-invariant system.

Template Parameters

StateDim	state dimension
InputDim	input dimension
OutputDim	output dimension

Given the following time-invariant linear discrete state equation.

\begin{align*} \boldsymbol{x}_{k+1} = \boldsymbol{A} \boldsymbol{x}_{k} + \boldsymbol{B} \boldsymbol{u}_{k} + \boldsymbol{e} \end{align*}

The following equation is called "sequential extension" here. In this class, the coefficients \(\boldsymbol{\hat{A}}\), \(\boldsymbol{\hat{B}}\), and \(\boldsymbol{\hat{e}}\) are calculated.

\begin{align*} \boldsymbol{\hat{x}}_{k+1} &= \boldsymbol{\hat{A}} \boldsymbol{x}_{k} + \boldsymbol{\hat{B}} \boldsymbol{\hat{u}}_{k} + \boldsymbol{\hat{e}} \\ \Leftrightarrow \begin{bmatrix} \boldsymbol{x}_{k+1} \\ \boldsymbol{x}_{k+2} \\ \boldsymbol{x}_{k+3} \\ \vdots \\ \boldsymbol{x}_{k+N} \end{bmatrix} &= \begin{bmatrix} \boldsymbol{A} \\ \boldsymbol{A}^2 \\ \boldsymbol{A}^3 \\ \vdots \\ \boldsymbol{A}^N \end{bmatrix} \boldsymbol{x}_{k} + \begin{bmatrix} \boldsymbol{B} & \boldsymbol{O} & \boldsymbol{O} & \boldsymbol{O} & \cdots & \boldsymbol{O} \\ \boldsymbol{A} \boldsymbol{B} & \boldsymbol{B} & \boldsymbol{O} & \boldsymbol{O} & \cdots & \boldsymbol{O} \\ \boldsymbol{A}^2 \boldsymbol{B} & \boldsymbol{A} \boldsymbol{B} & \boldsymbol{B} & \boldsymbol{O} & \cdots & \boldsymbol{O} \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ \boldsymbol{A}^{N-1} \boldsymbol{B} & \cdots & \cdots & \cdots & \boldsymbol{A} \boldsymbol{B} & \boldsymbol{B} \end{bmatrix} \begin{bmatrix} \boldsymbol{u}_{k} \\ \boldsymbol{u}_{k+1} \\ \boldsymbol{u}_{k+2} \\ \vdots \\ \boldsymbol{u}_{k+N-1} \end{bmatrix} + \begin{bmatrix} \boldsymbol{e} \\ (\boldsymbol{A} + \boldsymbol{I}) \boldsymbol{e} \\ (\boldsymbol{A}^2 + \boldsymbol{A} + \boldsymbol{I}) \boldsymbol{e} \\ \vdots \\ (\boldsymbol{A}^{N-1} + \cdots + \boldsymbol{A} + \boldsymbol{I}) \boldsymbol{e} \end{bmatrix} \end{align*}

Such a sequential extension is often used to formulate linear MPC as quadratic programming. For example, the following papers uses it.

PB Wieber. Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations. Humanoids, 2006.

Definition at line 61 of file InvariantSequentialExtension.h.

Member Typedef Documentation

◆ _StateSpaceModel

template<int StateDim, int InputDim, int OutputDim>

using CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::_StateSpaceModel = StateSpaceModel<StateDim, InputDim, OutputDim>

Type of state-space model with fixed dimensions of state, input, and output.

Definition at line 65 of file InvariantSequentialExtension.h.

Constructor & Destructor Documentation

◆ InvariantSequentialExtension()

template<int StateDim, int InputDim, int OutputDim>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::InvariantSequentialExtension	(	const std::shared_ptr< _StateSpaceModel > &	model,
		int	seq_len,
		bool	extend_for_output = `false`
	)

inline

Constructor.

Parameters

model	state-space model
seq_len	sequence length
extend_for_output	whether to extend for output instead of state

Definition at line 75 of file InvariantSequentialExtension.h.

Member Function Documentation

◆ setup()

template<int StateDim, int InputDim, int OutputDim>

void CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::setup ( bool extend_for_output )

inlineprotected

Setup coefficients.

Definition at line 103 of file InvariantSequentialExtension.h.

◆ totalInputDim()

template<int StateDim, int InputDim, int OutputDim>

int CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::totalInputDim ( ) const

inline

Get total input dimension.

Definition at line 90 of file InvariantSequentialExtension.h.

◆ totalOutputDim()

template<int StateDim, int InputDim, int OutputDim>

int CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::totalOutputDim ( ) const

inline

Get total output dimension.

Definition at line 96 of file InvariantSequentialExtension.h.

◆ totalStateDim()

template<int StateDim, int InputDim, int OutputDim>

int CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::totalStateDim ( ) const

inline

Get total state dimension.

Definition at line 84 of file InvariantSequentialExtension.h.

Member Data Documentation

◆ A_seq_

template<int StateDim, int InputDim, int OutputDim>

Eigen::Matrix<double, Eigen::Dynamic, StateDim> CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::A_seq_

Sequential extension matrix \(\boldsymbol{\hat{A}}\).

Definition at line 191 of file InvariantSequentialExtension.h.

◆ B_seq_

template<int StateDim, int InputDim, int OutputDim>

Eigen::MatrixXd CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::B_seq_

Sequential extension matrix \(\boldsymbol{\hat{B}}\).

Definition at line 194 of file InvariantSequentialExtension.h.

◆ E_seq_

template<int StateDim, int InputDim, int OutputDim>

Eigen::VectorXd CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::E_seq_

Sequential extension vector (i.e., offset vector) \(\boldsymbol{\hat{e}}\).

Definition at line 197 of file InvariantSequentialExtension.h.

◆ model_

template<int StateDim, int InputDim, int OutputDim>

std::shared_ptr<_StateSpaceModel> CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::model_

State-space model.

Definition at line 185 of file InvariantSequentialExtension.h.

◆ seq_len_

template<int StateDim, int InputDim, int OutputDim>

int CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >::seq_len_ = 0

Sequence length.

Definition at line 188 of file InvariantSequentialExtension.h.

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

/home/runner/work/CentroidalControlCollection/CentroidalControlCollection/catkin_ws/src/CentroidalControlCollection/include/CCC/InvariantSequentialExtension.h

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Detailed Description

template<int StateDim, int InputDim, int OutputDim> class CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >

Member Typedef Documentation

◆ _StateSpaceModel

Constructor & Destructor Documentation

◆ InvariantSequentialExtension()

Member Function Documentation

◆ setup()

◆ totalInputDim()

◆ totalOutputDim()

◆ totalStateDim()

Member Data Documentation

◆ A_seq_

◆ B_seq_

◆ E_seq_

◆ model_

◆ seq_len_

template<int StateDim, int InputDim, int OutputDim>
class CCC::InvariantSequentialExtension< StateDim, InputDim, OutputDim >