LQG with loop transform recovery
[kf,kc]=lqg_ltr(sl,mu,ro)
:sl linear system in state-space form ( syslin list) : :mu,ro real positive numbers chosen ``small enough’’ : :kf,kc controller and observer Kalman gains. :
returns the Kalman gains for:
x = a*x + b*u + l*w1
(sl)
y = c*x + mu*I*w2
z = h*x
Cost function:
/+oo
|
J = E(| [z(t)'*z(t) + ro^2*u(t)'*u(t)]dt)
`lqg`_ |
/ 0
The lqg/ltr approach looks for L,mu,H,ro such that: J(lqg) = J(freq) where
/+oo * * *
J = | tr[S W W S ] + tr[T T]dw
`freq`_ |
/0
and
S = (I + G*K)^(-1)
T = G*K*(I+G*K)^(-1)