LinearQuadraticRegulator< STATES, INPUTS > Class Template Reference

#include <linear_quadratic_regulator.h>

Public Member Functions
template<int OUTPUTS>
	LinearQuadraticRegulator (LinearSystem< STATES, INPUTS, OUTPUTS > &plant, const VectorX &Qtolerances, const VectorU &Rtolerances, const double &dt)
	LinearQuadraticRegulator (const MatrixA &A, const MatrixB &B, const VectorX &Qtolerances, const VectorU &Rtolerances, const double &dt)
	LinearQuadraticRegulator (const MatrixA &A, const MatrixB &B, const EMat< STATES, STATES > &Q, const EMat< INPUTS, INPUTS > &R, const double &dt)
VectorU	calculate (const VectorX &x, const VectorX &r)
template<int OUTPUTS>
void	latency_compensate (LinearSystem< STATES, INPUTS, OUTPUTS > &plant, const double &dt, const double &input_delay)

Detailed Description

template<int STATES, int INPUTS>
class LinearQuadraticRegulator< STATES, INPUTS >

Class implements an LQR controller. This finds the optimal gain matrix K where:

u = K(r - x)

K is optimized to minimize a cost function:

  ∞

J = ∑ xₖᵀQxₖ + uₖᵀRuₖ k=0

Where Q and R are the state and control cost matrices.

Template Parameters

STATES	The number of states in the system.
INPUTS	The number of inputs to the system.

Constructor & Destructor Documentation

LinearQuadraticRegulator() [1/3]

template<int STATES, int INPUTS>

template<int OUTPUTS>

LinearQuadraticRegulator< STATES, INPUTS >::LinearQuadraticRegulator ( LinearSystem< STATES, INPUTS, OUTPUTS > & plant, const VectorX & Qtolerances, const VectorU & Rtolerances, const double & dt )

inline

Constructs an LQR given a plant, a vector of tolerances for the states and inputs, and the timestep in seconds.

Template Parameters

OUTPUTS

The number of outputs of the plant.

Parameters

plant	The linear system to control.
Qtolerances	A vector of tolerances for each state.
Rtolerances	A vector of tolerances for each input.

LinearQuadraticRegulator() [2/3]

template<int STATES, int INPUTS>

LinearQuadraticRegulator< STATES, INPUTS >::LinearQuadraticRegulator ( const MatrixA & A, const MatrixB & B, const VectorX & Qtolerances, const VectorU & Rtolerances, const double & dt )

inline

Constructs an LQR given state and input matrices, a vector of tolerances for the states and inputs, and the timestep in seconds.

Parameters

A	The state matrix of the linear system.
B	The input matrix of the linear system.
Qtolerances	A vector of tolerances for each state.
Rtolerances	A vector of tolerances for each input.

LinearQuadraticRegulator() [3/3]

template<int STATES, int INPUTS>

LinearQuadraticRegulator< STATES, INPUTS >::LinearQuadraticRegulator ( const MatrixA & A, const MatrixB & B, const EMat< STATES, STATES > & Q, const EMat< INPUTS, INPUTS > & R, const double & dt )

inline

Constructs an LQR given state and input matrices, the cost matrices of states and inputs, and the timestep in seconds.

Parameters

A	The state matrix of the linear system.
B	The input matrix of the linear system.
Q	The cost matrix of the states.
R	The cost matrix of the inputs.

Member Function Documentation

calculate()

template<int STATES, int INPUTS>

VectorU LinearQuadraticRegulator< STATES, INPUTS >::calculate ( const VectorX & x, const VectorX & r )

inline

Computes the control input u as:

u = K(r - x)

Parameters

x	The current state.
r	The reference state.

latency_compensate()

template<int STATES, int INPUTS>

template<int OUTPUTS>

void LinearQuadraticRegulator< STATES, INPUTS >::latency_compensate ( LinearSystem< STATES, INPUTS, OUTPUTS > & plant, const double & dt, const double & input_delay )

inline

Recomputes K to work for a time delayed state.

Kdelay = K(A - BK)^(delay / dt)

Template Parameters

OUTPUTS

The number of outputs of the plant

Parameters

plant	The linear system.
dt	The timestep in seconds.
input_delay	The time delay of the system.

---

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

• linear_quadratic_regulator.h