Polytopic Luenberger Observer. More...

#include <polytopic_observer.hpp>

Public Types
using	Model = linalg::remove_cvref_t< Plant >

using	T = plant_type_t< Model >

using	State = plant_state_vec_t< Model >

using	QMat = linalg::Matrix< T, StateDim, StateDim >

using	WMat = linalg::Matrix< T, StateDim, OutputDim >

using	LMat = linalg::Matrix< T, StateDim, OutputDim >

using	FMat = QMat

using	ZSpace = linalg::RowVector< T, ZDim >

using	Fs = linalg::Vector< FMat, ZDim >

using	Polytope = linalg::Vector< Plant, N >

Public Member Functions
template<convex::AtomLike Var>
constexpr auto	operator() (const Polytope &poly, const Var &Z, T margin=1e-6) const
	operator overload (polytopic observer)

template<convex::AtomLike Var>
constexpr auto	apply (const Polytope &poly, const Var &Z, T margin=1e-6) const
	apply

template<convex::AtomLike ZVar>
constexpr auto	q_constraint (const ZVar &Z, T margin=1e-6) const
	q_constraint

template<convex::AtomLike ZVar>
constexpr auto	vertex_constraint (const Plant &plant, const ZVar &Z) const
	vertex constraint

constexpr auto	L (const QMat &Q, const WMat &W) const
	L.

Static Public Attributes
static constexpr std::size_t	StateDim = plant_traits<Model>::StateDim

static constexpr std::size_t	OutputDim = plant_traits<Model>::MeasurementDim

static constexpr std::size_t	QDim = StateDim * (StateDim + 1) / 2

static constexpr std::size_t	WDim = OutputDim * StateDim

static constexpr std::size_t	ZDim = QDim + WDim

Detailed Description

template<ContinuousPlantModelLike Plant, std::size_t N>
struct control::PolytopicObserver< Plant, N >

Polytopic Luenberger Observer.

Given xdot = A(t) x + B(t) u y = C(t) x

design a state observer xhatdot = A(t) xhat + B(t) u + L (y - C(t) xhat)

s.t. the estimation error e = x - xhat satisfies edot = (A(t) - L C(t)) e

There exists Q > 0 s.t. A_i^T Q + Q A_i - W C_i - C_i^T W^T < 0

where W = Q L, and L = Q^{-1} W.

Definition at line 41 of file polytopic_observer.hpp.

Member Typedef Documentation

◆ FMat

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::FMat = QMat

Definition at line 53 of file polytopic_observer.hpp.

◆ Fs

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::Fs = linalg::Vector<FMat, ZDim>

Definition at line 60 of file polytopic_observer.hpp.

◆ LMat

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::LMat = linalg::Matrix<T, StateDim, OutputDim>

Definition at line 52 of file polytopic_observer.hpp.

◆ Model

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::Model = linalg::remove_cvref_t<Plant>

Definition at line 42 of file polytopic_observer.hpp.

◆ Polytope

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::Polytope = linalg::Vector<Plant, N>

Definition at line 61 of file polytopic_observer.hpp.

◆ QMat

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::QMat = linalg::Matrix<T, StateDim, StateDim>

Definition at line 50 of file polytopic_observer.hpp.

◆ State

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::State = plant_state_vec_t<Model>

Definition at line 45 of file polytopic_observer.hpp.

◆ T

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::T = plant_type_t<Model>

Definition at line 44 of file polytopic_observer.hpp.

◆ WMat

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::WMat = linalg::Matrix<T, StateDim, OutputDim>

Definition at line 51 of file polytopic_observer.hpp.

◆ ZSpace

template<ContinuousPlantModelLike Plant, std::size_t N>

using control::PolytopicObserver< Plant, N >::ZSpace = linalg::RowVector<T, ZDim>

Definition at line 59 of file polytopic_observer.hpp.

Member Function Documentation

◆ apply()

template<ContinuousPlantModelLike Plant, std::size_t N>

template<convex::AtomLike Var>

constexpr auto control::PolytopicObserver< Plant, N >::apply	(	const Polytope &	poly,
		const Var &	Z,
		T	margin = `1e-6`
	)		const

inlineconstexpr

apply

Parameters

poly	(Polytope)
Z	([svec(Q); vec(W)])

Returns: PLDI as intersection of LMIs

Definition at line 86 of file polytopic_observer.hpp.

References control::is_continuous_v, control::PolytopicObserver< Plant, N >::q_constraint(), and control::PolytopicObserver< Plant, N >::vertex_constraint().

Referenced by control::PolytopicObserver< Plant, N >::operator()().

◆ L()

template<ContinuousPlantModelLike Plant, std::size_t N>

constexpr auto control::PolytopicObserver< Plant, N >::L	(	const QMat &	Q,
		const WMat &	W
	)		const

inlineconstexpr

L.

L = Q^{-1} W

Parameters

Q	(symmetric observability Gramian)
W	(lifted luenberger gain W = Q L)

Returns: L

Definition at line 175 of file polytopic_observer.hpp.

References control::is_continuous_v, and control::PolytopicObserver< Plant, N >::L().

Referenced by control::PolytopicObserver< Plant, N >::L().

◆ operator()()

template<ContinuousPlantModelLike Plant, std::size_t N>

template<convex::AtomLike Var>

constexpr auto control::PolytopicObserver< Plant, N >::operator()	(	const Polytope &	poly,
		const Var &	Z,
		T	margin = `1e-6`
	)		const

inlineconstexpr

operator overload (polytopic observer)

Parameters

poly	(Polytope)
Z	([svec(Q); vec(W)])

Returns: PLDI as intersection of LMIs

Definition at line 72 of file polytopic_observer.hpp.

References control::PolytopicObserver< Plant, N >::apply(), and control::is_continuous_v.

◆ q_constraint()

template<ContinuousPlantModelLike Plant, std::size_t N>

template<convex::AtomLike ZVar>

constexpr auto control::PolytopicObserver< Plant, N >::q_constraint	(	const ZVar &	Z,
		T	margin = `1e-6`
	)		const

inlineconstexpr

q_constraint

Parameters

Z	([svec(Q); vec(W)])
margin	(PDness)

Returns: LMI for Q

Definition at line 120 of file polytopic_observer.hpp.

References control::is_continuous_v, control::PolytopicObserver< Plant, N >::QDim, and control::PolytopicObserver< Plant, N >::WDim.

Referenced by control::PolytopicObserver< Plant, N >::apply().

◆ vertex_constraint()

template<ContinuousPlantModelLike Plant, std::size_t N>

template<convex::AtomLike ZVar>

constexpr auto control::PolytopicObserver< Plant, N >::vertex_constraint	(	const Plant &	plant,
		const ZVar &	Z
	)		const

inlineconstexpr

vertex constraint

Parameters

plant	(ModelPlant)
Z	(dec var)

Returns: LMI for the stability of each vertex

Definition at line 142 of file polytopic_observer.hpp.

References control::is_continuous_v, control::PolytopicObserver< Plant, N >::QDim, and control::PolytopicObserver< Plant, N >::WDim.

Referenced by control::PolytopicObserver< Plant, N >::apply().

Member Data Documentation

◆ OutputDim

template<ContinuousPlantModelLike Plant, std::size_t N>

constexpr std::size_t control::PolytopicObserver< Plant, N >::OutputDim = plant_traits<Model>::MeasurementDim

staticconstexpr

Definition at line 48 of file polytopic_observer.hpp.

◆ QDim

template<ContinuousPlantModelLike Plant, std::size_t N>

constexpr std::size_t control::PolytopicObserver< Plant, N >::QDim = StateDim * (StateDim + 1) / 2

staticconstexpr

Definition at line 55 of file polytopic_observer.hpp.

Referenced by control::PolytopicObserver< Plant, N >::q_constraint(), and control::PolytopicObserver< Plant, N >::vertex_constraint().

◆ StateDim

template<ContinuousPlantModelLike Plant, std::size_t N>

constexpr std::size_t control::PolytopicObserver< Plant, N >::StateDim = plant_traits<Model>::StateDim

staticconstexpr

Definition at line 47 of file polytopic_observer.hpp.

◆ WDim

template<ContinuousPlantModelLike Plant, std::size_t N>

constexpr std::size_t control::PolytopicObserver< Plant, N >::WDim = OutputDim * StateDim

staticconstexpr

Definition at line 56 of file polytopic_observer.hpp.

Referenced by control::PolytopicObserver< Plant, N >::q_constraint(), and control::PolytopicObserver< Plant, N >::vertex_constraint().

◆ ZDim

template<ContinuousPlantModelLike Plant, std::size_t N>

constexpr std::size_t control::PolytopicObserver< Plant, N >::ZDim = QDim + WDim

staticconstexpr

Definition at line 57 of file polytopic_observer.hpp.

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

include/akreon/control/estimation/polytopic_observer.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ FMat

◆ Fs

◆ LMat

◆ Model

◆ Polytope

◆ QMat

◆ State

◆ T

◆ WMat

◆ ZSpace

Member Function Documentation

◆ apply()

◆ L()

◆ operator()()

◆ q_constraint()

◆ vertex_constraint()

Member Data Documentation

◆ OutputDim

◆ QDim

◆ StateDim

◆ WDim

◆ ZDim