Package edu.wpi.first.math.jni

Class DAREJNI

java.lang.Object
edu.wpi.first.math.jni.WPIMathJNI
edu.wpi.first.math.jni.DAREJNI
public final class DAREJNI extends WPIMathJNI
DARE JNI.

  • Nested Class Summary

    Nested classes/interfaces inherited from class edu.wpi.first.math.jni.WPIMathJNI

    WPIMathJNI.Helper

  • Method Summary

    Modifier and Type
    Method
    Description
    static void
    dareABQR(double[] A, double[] B, double[] Q, double[] R, int states, int inputs, double[] S)
    Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.
    static void
    dareABQRN(double[] A, double[] B, double[] Q, double[] R, double[] N, int states, int inputs, double[] S)
    Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.
    static void
    dareNoPrecondABQR(double[] A, double[] B, double[] Q, double[] R, int states, int inputs, double[] S)
    Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.
    static void
    dareNoPrecondABQRN(double[] A, double[] B, double[] Q, double[] R, double[] N, int states, int inputs, double[] S)
    Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.

    Methods inherited from class edu.wpi.first.math.jni.WPIMathJNI

    forceLoad

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • dareNoPrecondABQR

      public static void dareNoPrecondABQR(double[] A, double[] B, double[] Q, double[] R, int states, int inputs, double[] S)
      Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.

      AᵀXA − X − AᵀXB(BᵀXB + R)⁻¹BᵀXA + Q = 0

      This internal function skips expensive precondition checks for increased performance. The solver may hang if any of the following occur:

      • Q isn't symmetric positive semidefinite
      • R isn't symmetric positive definite
      • The (A, B) pair isn't stabilizable
      • The (A, C) pair where Q = CᵀC isn't detectable

      Only use this function if you're sure the preconditions are met. Solves the discrete algebraic Riccati equation.

      Parameters:
      A - Array containing elements of A in row-major order.
      B - Array containing elements of B in row-major order.
      Q - Array containing elements of Q in row-major order.
      R - Array containing elements of R in row-major order.
      states - Number of states in A matrix.
      inputs - Number of inputs in B matrix.
      S - Array storage for DARE solution.

    • dareNoPrecondABQRN

      public static void dareNoPrecondABQRN(double[] A, double[] B, double[] Q, double[] R, double[] N, int states, int inputs, double[] S)
      Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.

      AᵀXA − X − (AᵀXB + N)(BᵀXB + R)⁻¹(BᵀXA + Nᵀ) + Q = 0

      This overload of the DARE is useful for finding the control law uₖ that minimizes the following cost function subject to xₖ₊₁ = Axₖ + Buₖ. 

           ∞ [xₖ]ᵀ[Q  N][xₖ]
 J = Σ [uₖ] [Nᵀ R][uₖ] ΔT
    k=0

      This is a more general form of the following. The linear-quadratic regulator is the feedback control law uₖ that minimizes the following cost function subject to xₖ₊₁ = Axₖ + Buₖ: 

           ∞
 J = Σ (xₖᵀQxₖ + uₖᵀRuₖ) ΔT
    k=0

      This can be refactored as: 

           ∞ [xₖ]ᵀ[Q 0][xₖ]
 J = Σ [uₖ] [0 R][uₖ] ΔT
    k=0

      This internal function skips expensive precondition checks for increased performance. The solver may hang if any of the following occur:

      • Q − NR⁻¹Nᵀ isn't symmetric positive semidefinite
      • R isn't symmetric positive definite
      • The (A − BR⁻¹Nᵀ, B) pair isn't stabilizable
      • The (A, C) pair where Q = CᵀC isn't detectable

      Only use this function if you're sure the preconditions are met.

      Parameters:
      A - Array containing elements of A in row-major order.
      B - Array containing elements of B in row-major order.
      Q - Array containing elements of Q in row-major order.
      R - Array containing elements of R in row-major order.
      N - Array containing elements of N in row-major order.
      states - Number of states in A matrix.
      inputs - Number of inputs in B matrix.
      S - Array storage for DARE solution.

    • dareABQR

      public static void dareABQR(double[] A, double[] B, double[] Q, double[] R, int states, int inputs, double[] S)
      Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.

      AᵀXA − X − AᵀXB(BᵀXB + R)⁻¹BᵀXA + Q = 0

      Parameters:
      A - Array containing elements of A in row-major order.
      B - Array containing elements of B in row-major order.
      Q - Array containing elements of Q in row-major order.
      R - Array containing elements of R in row-major order.
      states - Number of states in A matrix.
      inputs - Number of inputs in B matrix.
      S - Array storage for DARE solution.
      Throws:
      IllegalArgumentException - if Q isn't symmetric positive semidefinite.
      IllegalArgumentException - if R isn't symmetric positive definite.
      IllegalArgumentException - if the (A, B) pair isn't stabilizable.
      IllegalArgumentException - if the (A, C) pair where Q = CᵀC isn't detectable.

    • dareABQRN

      public static void dareABQRN(double[] A, double[] B, double[] Q, double[] R, double[] N, int states, int inputs, double[] S)
      Computes the unique stabilizing solution X to the discrete-time algebraic Riccati equation.

      AᵀXA − X − (AᵀXB + N)(BᵀXB + R)⁻¹(BᵀXA + Nᵀ) + Q = 0

      This overload of the DARE is useful for finding the control law uₖ that minimizes the following cost function subject to xₖ₊₁ = Axₖ + Buₖ. 

           ∞ [xₖ]ᵀ[Q  N][xₖ]
 J = Σ [uₖ] [Nᵀ R][uₖ] ΔT
    k=0

      This is a more general form of the following. The linear-quadratic regulator is the feedback control law uₖ that minimizes the following cost function subject to xₖ₊₁ = Axₖ + Buₖ: 

           ∞
 J = Σ (xₖᵀQxₖ + uₖᵀRuₖ) ΔT
    k=0

      This can be refactored as: 

           ∞ [xₖ]ᵀ[Q 0][xₖ]
 J = Σ [uₖ] [0 R][uₖ] ΔT
    k=0
      Parameters:
      A - Array containing elements of A in row-major order.
      B - Array containing elements of B in row-major order.
      Q - Array containing elements of Q in row-major order.
      R - Array containing elements of R in row-major order.
      N - Array containing elements of N in row-major order.
      states - Number of states in A matrix.
      inputs - Number of inputs in B matrix.
      S - Array storage for DARE solution.
      Throws:
      IllegalArgumentException - if Q − NR⁻¹Nᵀ isn't symmetric positive semidefinite.
      IllegalArgumentException - if R isn't symmetric positive definite.
      IllegalArgumentException - if the (A − BR⁻¹Nᵀ, B) pair isn't stabilizable.
      IllegalArgumentException - if the (A, C) pair where Q = CᵀC isn't detectable.