control Namespace Reference

Classes
struct	H2PolytopicStateFeedback
	H2 Polytopic State Feedback. More...
struct	H2PolytopicStateObserver
	H2 Polytopic State Observer. More...
struct	H2StateFeedback
	H2 State Feedback. More...
struct	H2StateObserver
	H2 State Observer. More...
struct	HinfPolytopicStateFeedback
	Hinf Polytopic State Feedback. More...
struct	HinfPolytopicStateObserver
	Hinf Polytopic State Observer. More...
struct	HinfStateFeedback
	Hinf State Feedback. More...
struct	HinfStateObserver
	Hinf State Observer. More...
struct	LuenbergerObserver
	Luenberger Observer. More...
struct	plant_traits
	base type traits for plant model More...
struct	plant_traits< PlantModel< SS, InputPortsT, OutputPortsT > >
	explicit type traits for plant model More...
struct	PlantModel
	Forward declaration of PlantModel. More...
struct	PolytopicObserver
	Polytopic Luenberger Observer. More...
struct	PolytopicStateFeedback
	PolytopicStateFeedback. More...
struct	Port
	Port specification. More...
struct	PortLayout
	Port layout over either the state-space input or output axis. More...
struct	ss_traits
	base type traits for state space More...
struct	ss_traits< StateSpace< Type, PlantIn, ControlIn, OutputIn > >
	explicit type traits for state space More...
struct	StateFeedback
	StateFeedback. More...
struct	StateSpace
	forward decl of state space More...

Concepts
concept	PortLike
concept	StateSpaceLike
	StateSpace concept.
concept	ContinuousStateSpaceLike
	ContinuousStateSpace concept.
concept	DiscreteStateSpaceLike
	ContinuousStateSpace concept.
concept	PlantModelLike
	PlantModel concept.
concept	ContinuousPlantModelLike
	ContinuousPlantModel concept.
concept	DiscretePlantModelLike
	DiscretePlantModel concept.

Typedefs
template<typename StateSpace >
using	ss_type_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::T
	extract scalar type from ss
template<typename StateSpace >
using	ss_plant_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::Plant
	ss plant type
template<typename StateSpace >
using	ss_control_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::Control
	ss control type
template<typename StateSpace >
using	ss_output_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::Output
	ss output type
template<typename StateSpace >
using	state_vec_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::State
	extract state vector
template<typename StateSpace >
using	input_vec_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::Input
	extract input vector
template<typename StateSpace >
using	output_vec_t = typename ss_traits< linalg::remove_cvref_t< StateSpace > >::OutVec
	extract output vector
template<typename Plant >
using	plant_type_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::T
	extract scalar type from plant
template<typename Plant >
using	plant_state_space_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::StateSpace
	extract state-space type from plant
template<typename Plant >
using	plant_input_ports_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::InputPorts
	extract input port layout type from plant
template<typename Plant >
using	plant_output_ports_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::OutputPorts
	extract output port layout type from plant
template<typename Plant >
using	plant_state_vec_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::State
	extract state vector from plant
template<typename Plant >
using	plant_input_vec_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::Input
	extract full input vector from plant
template<typename Plant >
using	plant_output_vec_t = typename plant_traits< linalg::remove_cvref_t< Plant > >::Output
	extract full output vector from plant

Enumerations
enum struct	PortRole : uint8_t { EXOGENOUS , CONTROL , PERFORMANCE , MEASUREMENT }
	Plant port role. More...
enum struct	TimeDomainType : uint8_t { CONTINUOUS = 0 , DISCRETE }
	time domain type More...

Functions
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>
constexpr auto	make_h2_polytopic_state_observer_problem (const linalg::Vector< Plant, N > &poly, const DecVar &Z_hat, plant_type_t< Plant > margin=1e-6)
	make polytopic state observer
template<ContinuousPlantModelLike ObsModel, convex::AtomLike DecVar>
constexpr auto	make_h2_state_observer_problem (const ObsModel &model, const DecVar &Z_hat, plant_type_t< ObsModel > margin=1e-6)
	make h2 state observer problem
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>
constexpr auto	make_hinf_polytopic_state_observer_problem (const linalg::Vector< Plant, N > &poly, const DecVar &Z_hat, plant_type_t< Plant > margin=1e-6)
	make polytopic Hinf state observer
template<ContinuousPlantModelLike ObsModel, convex::AtomLike DecVar>
constexpr auto	make_hinf_state_observer_problem (const ObsModel &model, const DecVar &Z_hat, plant_type_t< ObsModel > margin=1e-6)
	make hinf state observer problem
template<ContinuousPlantModelLike ObsModel, convex::AtomLike ZVar>
constexpr auto	make_observer_problem (const ObsModel &model, const ZVar &Z, const auto &obj, plant_type_t< ObsModel > margin=1e-6)
	make observer problem
template<ContinuousPlantModelLike ObsModel, convex::AtomLike ZVar>
constexpr auto	make_observer_problem (const ObsModel &model, const ZVar &Z, plant_type_t< ObsModel > margin=1e-6)
	make observer problem
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_observer_quadratic_objective (const linalg::Matrix< plant_type_t< Plant >, PolytopicObserver< Plant, N >::ZDim, PolytopicObserver< Plant, N >::ZDim > &P, const linalg::Vector< plant_type_t< Plant >, PolytopicObserver< Plant, N >::ZDim > &q, const ZVar &Z)
	make quadratic objective over merged PLDI variable
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_observer_problem (const linalg::Vector< Plant, N > &poly, const ZVar &Z, const auto &obj, plant_type_t< Plant > margin=1e-6)
	make PLDI problem with objective
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_observer_problem (const linalg::Vector< Plant, N > &poly, const ZVar &Z, plant_type_t< Plant > margin=1e-6)
	make PLDI feasibility problem
template<linalg::SquareMatrix PMat, linalg::MatrixContainer YMat>
constexpr auto	recover_state_feedback_gain (const PMat &P, const YMat &Y)
	recover state-feedback gain from a lifted gain variable
template<linalg::SquareMatrix QMat, linalg::MatrixContainer WMat>
constexpr auto	recover_state_observer_gain (const QMat &Q, const WMat &W)
	recover state-observer gain from a lifted gain variable
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>
constexpr auto	make_h2_polytopic_state_feedback_problem (const linalg::Vector< Plant, N > &poly, const DecVar &Z_hat, plant_type_t< Plant > margin=1e-6)
	make polytopic H2
template<ContinuousPlantModelLike SFModel, convex::AtomLike DecVar>
constexpr auto	make_h2_state_feedback_problem (const SFModel &model, const DecVar &Z_hat, plant_type_t< SFModel > margin=1e-6)
	make h2 state feedback problem
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>
constexpr auto	make_hinf_polytopic_state_feedback_problem (const linalg::Vector< Plant, N > &poly, const DecVar &Z_hat, plant_type_t< Plant > margin=1e-6)
	make polytopic Hinf state feedback
template<ContinuousPlantModelLike SFModel, convex::AtomLike DecVar>
constexpr auto	make_hinf_state_feedback_problem (const SFModel &model, const DecVar &Z_hat, plant_type_t< SFModel > margin=1e-6)
	make hinf state feedback problem
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_state_feedback_linear_objective (const linalg::Vector< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::PDim > &p_weights, const linalg::Vector< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::YDim > &y_weights, const ZVar &Z)
	make linear objective over merged PLDI variable
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_state_feedback_quadratic_objective (const linalg::Matrix< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::ZDim, PolytopicStateFeedback< Plant, N >::ZDim > &P, const linalg::Vector< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::ZDim > &q, const ZVar &Z)
	make quadratic objective over merged PLDI variable
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_state_feedback_problem (const linalg::Vector< Plant, N > &poly, const ZVar &Z, const auto &obj, plant_type_t< Plant > margin=1e-6)
	make PLDI problem with objective
template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>
constexpr auto	make_polytopic_state_feedback_problem (const linalg::Vector< Plant, N > &poly, const ZVar &Z, plant_type_t< Plant > margin=1e-6)
	make PLDI feasibility problem
template<ContinuousPlantModelLike SFModel, convex::AtomLike ZVar>
constexpr auto	make_state_feedback_problem (const SFModel &model, const ZVar &Z, const auto &obj, plant_type_t< SFModel > margin=1e-6)
	make state feedback problem
template<ContinuousPlantModelLike SFModel, convex::AtomLike ZVar>
constexpr auto	make_state_feedback_problem (const SFModel &model, const ZVar &Z, plant_type_t< SFModel > margin=1e-6)
	make state feedback feasibility problem
template<ContinuousStateSpaceLike SS> requires linalg::Real<ss_type_t<SS>>
constexpr auto	c2d_zoh (const SS &continuous, ss_type_t< SS > dt)
	Convert a real continuous state-space model using zero-order hold.

Variables
template<typename StateSpace >
constexpr bool	is_continuous_v
	check if continuous or not
template<typename Plant >
constexpr bool	plant_is_continuous_v
	check if plant model is continuous

Typedef Documentation

input_vec_t

template<typename StateSpace >

using control::input_vec_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::Input

extract input vector

Definition at line 165 of file control_traits.hpp.

output_vec_t

template<typename StateSpace >

using control::output_vec_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::OutVec

extract output vector

Definition at line 170 of file control_traits.hpp.

plant_input_ports_t

template<typename Plant >

using control::plant_input_ports_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::InputPorts

extract input port layout type from plant

Definition at line 244 of file control_traits.hpp.

plant_input_vec_t

template<typename Plant >

using control::plant_input_vec_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::Input

extract full input vector from plant

Definition at line 259 of file control_traits.hpp.

plant_output_ports_t

template<typename Plant >

using control::plant_output_ports_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::OutputPorts

extract output port layout type from plant

Definition at line 249 of file control_traits.hpp.

plant_output_vec_t

template<typename Plant >

using control::plant_output_vec_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::Output

extract full output vector from plant

Definition at line 264 of file control_traits.hpp.

plant_state_space_t

template<typename Plant >

using control::plant_state_space_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::StateSpace

extract state-space type from plant

Definition at line 239 of file control_traits.hpp.

plant_state_vec_t

template<typename Plant >

using control::plant_state_vec_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::State

extract state vector from plant

Definition at line 254 of file control_traits.hpp.

plant_type_t

template<typename Plant >

using control::plant_type_t = typedef typename plant_traits<linalg::remove_cvref_t<Plant> >::T

extract scalar type from plant

Definition at line 235 of file control_traits.hpp.

ss_control_t

template<typename StateSpace >

using control::ss_control_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::Control

ss control type

Definition at line 150 of file control_traits.hpp.

ss_output_t

template<typename StateSpace >

using control::ss_output_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::Output

ss output type

Definition at line 155 of file control_traits.hpp.

ss_plant_t

template<typename StateSpace >

using control::ss_plant_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::Plant

ss plant type

Definition at line 145 of file control_traits.hpp.

ss_type_t

template<typename StateSpace >

using control::ss_type_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::T

extract scalar type from ss

Definition at line 141 of file control_traits.hpp.

state_vec_t

template<typename StateSpace >

using control::state_vec_t = typedef typename ss_traits<linalg::remove_cvref_t<StateSpace> >::State

extract state vector

Definition at line 160 of file control_traits.hpp.

Enumeration Type Documentation

PortRole

enum struct control::PortRole : uint8_t

strong

Plant port role.

Enumerator
EXOGENOUS	w: disturbance, reference, noise, or other external input
CONTROL	u: controller input to the plant
PERFORMANCE	z: regulated/performance output
MEASUREMENT	y: measured output available for feedback/estimation

Definition at line 17 of file control_traits.hpp.

TimeDomainType

enum struct control::TimeDomainType : uint8_t

strong

time domain type

Enumerator
CONTINUOUS
DISCRETE

Definition at line 113 of file control_traits.hpp.

Function Documentation

c2d_zoh()

template<ContinuousStateSpaceLike SS>
requires linalg::Real<ss_type_t<SS>>

constexpr auto control::c2d_zoh ( const SS &  continuous, ss_type_t< SS >  dt  )

constexpr

Convert a real continuous state-space model using zero-order hold.

For xdot = A*x + B*u, hold u(t) = u_k over [k*dt, (k+1)*dt). Integrating the dynamics gives x_(k+1) = Ad*x_k + Bd*u_k, where Ad = exp(A*dt), Bd = integral_0^dt exp(A*tau)*B d(tau). Compute both through exp(dt * [A B; 0 0]) = [Ad Bd; 0 I], avoiding an inverse of A so integrators and other singular A are supported. For y = C*x + D*u, sampled outputs retain Cd = C and Dd = D; an absent D remains absent. Inputs are held constant over each sample interval; dt is in the same time units as the continuous dynamics. The returned StateSpace does not store dt. Accuracy follows linalg::matrix_exp's generalized-eigenvector algorithm.

Exceptions

std::invalid_argument	Nonfinite model or nonpositive/nonfinite dt.
std::runtime_error	Nonfinite, nonreal, or structurally invalid matrix exponential (including its zero-matrix failure sentinel).

Definition at line 38 of file discretization.hpp.

References is_continuous_v.

make_h2_polytopic_state_feedback_problem()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>

constexpr auto control::make_h2_polytopic_state_feedback_problem ( const linalg::Vector< Plant, N > &  poly, const DecVar &  Z_hat, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make polytopic H2

Parameters

poly	(Polytope of plant models)
Z_hat	(dec var)
margin	(PDness

Returns

H2 problem

Definition at line 131 of file h2_polytopic_state_feedback.hpp.

References is_continuous_v.

make_h2_polytopic_state_observer_problem()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>

constexpr auto control::make_h2_polytopic_state_observer_problem ( const linalg::Vector< Plant, N > &  poly, const DecVar &  Z_hat, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make polytopic state observer

Parameters

poly	(Polytope of plant models)
Z_hat	(Dec Var)
margin	(for PD)

Returns

convex problem

Definition at line 132 of file h2_polytopic_state_observer.hpp.

References is_continuous_v.

make_h2_state_feedback_problem()

template<ContinuousPlantModelLike SFModel, convex::AtomLike DecVar>

constexpr auto control::make_h2_state_feedback_problem ( const SFModel &  model, const DecVar &  Z_hat, plant_type_t< SFModel >  margin = 1e-6  )

constexpr

make h2 state feedback problem

Parameters

model	(PlantModel)
Z	(DecVar)
margin	(PSD Margin)

Returns

h2 state feedback problem

Definition at line 282 of file h2_state_feedback.hpp.

References is_continuous_v.

make_h2_state_observer_problem()

template<ContinuousPlantModelLike ObsModel, convex::AtomLike DecVar>

constexpr auto control::make_h2_state_observer_problem ( const ObsModel &  model, const DecVar &  Z_hat, plant_type_t< ObsModel >  margin = 1e-6  )

constexpr

make h2 state observer problem

Parameters

model	(PlantModel)
Z	(DecVar)
margin	(PSD Margin)

Returns

h2 state observer problem

Definition at line 290 of file h2_state_observer.hpp.

References is_continuous_v.

make_hinf_polytopic_state_feedback_problem()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>

constexpr auto control::make_hinf_polytopic_state_feedback_problem ( const linalg::Vector< Plant, N > &  poly, const DecVar &  Z_hat, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make polytopic Hinf state feedback

Parameters

poly	(Polytope of plant models)
Z_hat	(dec var)
margin	(PDness)

Returns

Hinf problem

Definition at line 131 of file hinf_polytopic_state_feedback.hpp.

References is_continuous_v.

make_hinf_polytopic_state_observer_problem()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike DecVar>

constexpr auto control::make_hinf_polytopic_state_observer_problem ( const linalg::Vector< Plant, N > &  poly, const DecVar &  Z_hat, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make polytopic Hinf state observer

Parameters

poly	(Polytope of plant models)
Z_hat	(dec var)
margin	(for PD)

Returns

Hinf problem

Definition at line 131 of file hinf_polytopic_state_observer.hpp.

References is_continuous_v.

make_hinf_state_feedback_problem()

template<ContinuousPlantModelLike SFModel, convex::AtomLike DecVar>

constexpr auto control::make_hinf_state_feedback_problem ( const SFModel &  model, const DecVar &  Z_hat, plant_type_t< SFModel >  margin = 1e-6  )

constexpr

make hinf state feedback problem

Parameters

model	(PlantModel)
Z_hat	(DecVar)
margin	(PSD margin)

Returns

hinf state feedback problem

Definition at line 321 of file hinf_state_feedback.hpp.

References is_continuous_v.

make_hinf_state_observer_problem()

template<ContinuousPlantModelLike ObsModel, convex::AtomLike DecVar>

constexpr auto control::make_hinf_state_observer_problem ( const ObsModel &  model, const DecVar &  Z_hat, plant_type_t< ObsModel >  margin = 1e-6  )

constexpr

make hinf state observer problem

Parameters

model	(PlantModel)
Z_hat	(DecVar)
margin	(PSD margin)

Returns

hinf state observer problem

Definition at line 304 of file hinf_state_observer.hpp.

References is_continuous_v.

make_observer_problem() [1/2]

template<ContinuousPlantModelLike ObsModel, convex::AtomLike ZVar>

constexpr auto control::make_observer_problem ( const ObsModel &  model, const ZVar &  Z, const auto &  obj, plant_type_t< ObsModel >  margin = 1e-6  )

constexpr

make observer problem

Parameters

model	(StateSpace)
Q	(Var)
obj	(Objective)
margin	(PSD margin)

Returns

observer problem

Definition at line 185 of file luenberger_observer.hpp.

References is_continuous_v.

make_observer_problem() [2/2]

template<ContinuousPlantModelLike ObsModel, convex::AtomLike ZVar>

constexpr auto control::make_observer_problem ( const ObsModel &  model, const ZVar &  Z, plant_type_t< ObsModel >  margin = 1e-6  )

constexpr

make observer problem

Parameters

model	(StateSpace)
Q	(Var)
margin	(PSD margin)

Returns

observer problem

Definition at line 206 of file luenberger_observer.hpp.

References is_continuous_v.

make_polytopic_observer_problem() [1/2]

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_observer_problem ( const linalg::Vector< Plant, N > &  poly, const ZVar &  Z, const auto &  obj, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make PLDI problem with objective

Parameters

poly	polytope vertices
Z	merged decision var [svec(Q); vec(W)]
obj	objective atom over merged var
margin	PSD margin on Q block

Returns

PLDI optimization problem

Definition at line 215 of file polytopic_observer.hpp.

References is_continuous_v.

make_polytopic_observer_problem() [2/2]

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_observer_problem ( const linalg::Vector< Plant, N > &  poly, const ZVar &  Z, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make PLDI feasibility problem

Parameters

poly	polytope vertices
Z	merged decision var [svec(Q); vec(W)]
margin	PSD margin on Q block

Returns

PLDI feasibility problem

Definition at line 232 of file polytopic_observer.hpp.

References is_continuous_v.

make_polytopic_observer_quadratic_objective()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_observer_quadratic_objective ( const linalg::Matrix< plant_type_t< Plant >, PolytopicObserver< Plant, N >::ZDim, PolytopicObserver< Plant, N >::ZDim > &  P, const linalg::Vector< plant_type_t< Plant >, PolytopicObserver< Plant, N >::ZDim > &  q, const ZVar &  Z  )

constexpr

make quadratic objective over merged PLDI variable

obj(z) = 0.5 z^T P z + q^T z

Parameters

P	quadratic weight over merged z
q	linear weight over merged z
Z	merged decision var

Returns

quadratic objective atom

Definition at line 195 of file polytopic_observer.hpp.

References is_continuous_v.

make_polytopic_state_feedback_linear_objective()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_state_feedback_linear_objective ( const linalg::Vector< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::PDim > &  p_weights, const linalg::Vector< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::YDim > &  y_weights, const ZVar &  Z  )

constexpr

make linear objective over merged PLDI variable

obj(z) = p_w^T svec(P) + y_w^T vec(Y)

Parameters

p_weights	weights over svec(P)
y_weights	weights over vec(Y)
Z	merged decision var

Returns

linear objective atom

Definition at line 131 of file polytopic_state_feedback.hpp.

References is_continuous_v.

make_polytopic_state_feedback_problem() [1/2]

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_state_feedback_problem ( const linalg::Vector< Plant, N > &  poly, const ZVar &  Z, const auto &  obj, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make PLDI problem with objective

Parameters

poly	polytope vertices
Z	merged decision var [svec(P); vec(Y)]
obj	objective atom over merged var
margin	PSD margin on P block

Returns

PLDI optimization problem

Definition at line 180 of file polytopic_state_feedback.hpp.

References is_continuous_v.

make_polytopic_state_feedback_problem() [2/2]

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_state_feedback_problem ( const linalg::Vector< Plant, N > &  poly, const ZVar &  Z, plant_type_t< Plant >  margin = 1e-6  )

constexpr

make PLDI feasibility problem

Parameters

poly	polytope vertices
Z	merged decision var [svec(P); vec(Y)]
margin	PSD margin on P block

Returns

PLDI feasibility problem

Definition at line 197 of file polytopic_state_feedback.hpp.

References is_continuous_v.

make_polytopic_state_feedback_quadratic_objective()

template<ContinuousPlantModelLike Plant, std::size_t N, convex::AtomLike ZVar>

constexpr auto control::make_polytopic_state_feedback_quadratic_objective ( const linalg::Matrix< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::ZDim, PolytopicStateFeedback< Plant, N >::ZDim > &  P, const linalg::Vector< plant_type_t< Plant >, PolytopicStateFeedback< Plant, N >::ZDim > &  q, const ZVar &  Z  )

constexpr

make quadratic objective over merged PLDI variable

obj(z) = 0.5 z^T P z + q^T z

Parameters

P	quadratic weight over merged z
q	linear weight over merged z
Z	merged decision var

Returns

quadratic objective atom

Definition at line 159 of file polytopic_state_feedback.hpp.

References is_continuous_v.

make_state_feedback_problem() [1/2]

template<ContinuousPlantModelLike SFModel, convex::AtomLike ZVar>

constexpr auto control::make_state_feedback_problem ( const SFModel &  model, const ZVar &  Z, const auto &  obj, plant_type_t< SFModel >  margin = 1e-6  )

constexpr

make state feedback problem

Parameters

model	(StateSpace)
Z	(merged decision var [svec(P); vec(Y)])
obj	(objective)
margin	(PSD margin)

Returns

state feedback problem

Definition at line 190 of file state_feedback.hpp.

References is_continuous_v.

make_state_feedback_problem() [2/2]

template<ContinuousPlantModelLike SFModel, convex::AtomLike ZVar>

constexpr auto control::make_state_feedback_problem ( const SFModel &  model, const ZVar &  Z, plant_type_t< SFModel >  margin = 1e-6  )

constexpr

make state feedback feasibility problem

Parameters

model	(StateSpace)
Z	(merged decision var [svec(P); vec(Y)])
margin	(PSD margin)

Returns

state feedback feasibility problem

Definition at line 209 of file state_feedback.hpp.

References is_continuous_v.

recover_state_feedback_gain()

template<linalg::SquareMatrix PMat, linalg::MatrixContainer YMat>

constexpr auto control::recover_state_feedback_gain ( const PMat &  P, const YMat &  Y  )

constexpr

recover state-feedback gain from a lifted gain variable

For standard state feedback and H2 state feedback, the lifted variable has the same form:

Y = K P K = Y P^{-1}

Parameters

P	symmetric positive-definite controllability Gramian block
Y	lifted feedback product

Returns

tuple(K, numerical event)

Definition at line 27 of file gain_recovery.hpp.

References is_continuous_v.

Referenced by control::StateFeedback< SFModel >::K(), control::H2StateFeedback< SFModel >::K(), and control::HinfStateFeedback< SFModel >::K().

recover_state_observer_gain()

template<linalg::SquareMatrix QMat, linalg::MatrixContainer WMat>

constexpr auto control::recover_state_observer_gain ( const QMat &  Q, const WMat &  W  )

constexpr

recover state-observer gain from a lifted gain variable

For H2 state observers, the lifted variable has the form:

W = Q L L = Q^{-1} W

Parameters

Q	symmetric positive-definite observability Gramian block
W	lifted observer product

Returns

tuple(L, numerical event)

Definition at line 57 of file gain_recovery.hpp.

References is_continuous_v.

Referenced by control::H2StateObserver< ObsModel >::L(), control::HinfStateObserver< ObsModel >::L(), and control::LuenbergerObserver< ObsModel >::L().

Variable Documentation

is_continuous_v

template<typename StateSpace >

constexpr bool control::is_continuous_v

inlineconstexpr

Initial value:

=
    ss_traits<linalg::remove_cvref_t<StateSpace>>::DType ==
    TimeDomainType::CONTINUOUS

check if continuous or not

Definition at line 175 of file control_traits.hpp.

Referenced by control::H2StateObserver< ObsModel >::apply(), control::HinfStateObserver< ObsModel >::apply(), control::LuenbergerObserver< ObsModel >::apply(), control::H2PolytopicStateObserver< Plant, N >::apply(), control::HinfPolytopicStateObserver< Plant, N >::apply(), control::H2PolytopicStateFeedback< Plant, N >::apply(), control::HinfPolytopicStateFeedback< Plant, N >::apply(), control::PolytopicObserver< Plant, N >::apply(), control::PolytopicStateFeedback< Plant, N >::apply(), control::H2StateFeedback< SFModel >::apply(), control::HinfStateFeedback< SFModel >::apply(), control::StateFeedback< SFModel >::apply(), control::HinfStateObserver< ObsModel >::brl_constraint(), control::HinfStateFeedback< SFModel >::brl_constraint(), c2d_zoh(), control::PlantModel< SS, InputPorts, OutputPorts >::control_matrix(), control::PlantModel< SS, InputPorts, OutputPorts >::exogenous_matrix(), control::PlantModel< SS, InputPorts, OutputPorts >::feedthrough(), control::PolytopicStateFeedback< Plant, N >::K(), control::StateFeedback< SFModel >::K(), control::H2PolytopicStateFeedback< Plant, N >::K(), control::H2StateFeedback< SFModel >::K(), control::HinfPolytopicStateFeedback< Plant, N >::K(), control::HinfStateFeedback< SFModel >::K(), control::H2PolytopicStateObserver< Plant, N >::L(), control::H2StateObserver< ObsModel >::L(), control::HinfPolytopicStateObserver< Plant, N >::L(), control::HinfStateObserver< ObsModel >::L(), control::LuenbergerObserver< ObsModel >::L(), control::PolytopicObserver< Plant, N >::L(), make_h2_polytopic_state_feedback_problem(), make_h2_polytopic_state_observer_problem(), make_h2_state_feedback_problem(), make_h2_state_observer_problem(), make_hinf_polytopic_state_feedback_problem(), make_hinf_polytopic_state_observer_problem(), make_hinf_state_feedback_problem(), make_hinf_state_observer_problem(), make_observer_problem(), make_observer_problem(), make_polytopic_observer_problem(), make_polytopic_observer_problem(), make_polytopic_observer_quadratic_objective(), make_polytopic_state_feedback_linear_objective(), make_polytopic_state_feedback_problem(), make_polytopic_state_feedback_problem(), make_polytopic_state_feedback_quadratic_objective(), make_state_feedback_problem(), make_state_feedback_problem(), control::PlantModel< SS, InputPorts, OutputPorts >::measurement_matrix(), control::H2PolytopicStateObserver< Plant, N >::objective(), control::H2StateObserver< ObsModel >::objective(), control::HinfPolytopicStateObserver< Plant, N >::objective(), control::HinfStateObserver< ObsModel >::objective(), control::H2PolytopicStateFeedback< Plant, N >::objective(), control::H2StateFeedback< SFModel >::objective(), control::HinfPolytopicStateFeedback< Plant, N >::objective(), control::HinfStateFeedback< SFModel >::objective(), control::H2StateObserver< ObsModel >::operator()(), control::HinfStateObserver< ObsModel >::operator()(), control::LuenbergerObserver< ObsModel >::operator()(), control::H2PolytopicStateObserver< Plant, N >::operator()(), control::HinfPolytopicStateObserver< Plant, N >::operator()(), control::H2PolytopicStateFeedback< Plant, N >::operator()(), control::HinfPolytopicStateFeedback< Plant, N >::operator()(), control::PolytopicObserver< Plant, N >::operator()(), control::PolytopicStateFeedback< Plant, N >::operator()(), control::H2StateFeedback< SFModel >::operator()(), control::HinfStateFeedback< SFModel >::operator()(), control::StateFeedback< SFModel >::operator()(), control::StateSpace< Type, PlantIn, ControlIn, OutputIn >::output_map(), control::StateFeedback< SFModel >::p_constraint(), control::PlantModel< SS, InputPorts, OutputPorts >::performance_matrix(), control::HinfStateObserver< ObsModel >::q_constraint(), control::HinfStateFeedback< SFModel >::q_constraint(), control::LuenbergerObserver< ObsModel >::q_constraint(), control::PolytopicObserver< Plant, N >::q_constraint(), recover_state_feedback_gain(), recover_state_observer_gain(), control::H2StateObserver< ObsModel >::stability_constraint(), control::LuenbergerObserver< ObsModel >::stability_constraint(), control::H2StateFeedback< SFModel >::stability_constraint(), control::StateFeedback< SFModel >::stability_constraint(), control::StateSpace< Type, PlantIn, ControlIn, OutputIn >::state_update(), control::PolytopicObserver< Plant, N >::vertex_constraint(), control::H2StateObserver< ObsModel >::z_constraint(), and control::H2StateFeedback< SFModel >::z_constraint().

plant_is_continuous_v

template<typename Plant >

constexpr bool control::plant_is_continuous_v

inlineconstexpr

Initial value:

=
    plant_traits<linalg::remove_cvref_t<Plant>>::DType ==
    TimeDomainType::CONTINUOUS

check if plant model is continuous

Definition at line 280 of file control_traits.hpp.