ControlSystems: dlqr method

Specific Domains Modelling & Simulations
1

I’m a little confused by the “docstring”/documentation of dlqr:

  dlqr(A, B, Q, R), dlqr(sys, Q, R)

  Calculate the optimal gain matrix K for the state-feedback law u[k] = K*x[k] that minimizes the cost function:

  J = sum(x'Qx + u'Ru, 0, inf).

  For the discrte time model x[k+1] = Ax[k] + Bu[k].

  See also lqg

  Usage example:

  h = 0.1
  A = [1 h; 0 1]
  B = [0;1]
  C = [1 0]
  sys = ss(A,B,C,0, h)
  Q = eye(2)
  R = eye(1)
  L = dlqr(A,B,Q,R) # lqr(sys,Q,R) can also be used

  u(t,x) = -L*x # Form control law,

The introduction talks about computing matrix K and positive feedback u=Kx while the example states that matrix L is computed where presumably L=-K.

I assume this is just a question of typos/documentation in need of update?

2

Correct