— Function File: [k, q1, p1, ee, er] = lqg (sys, sigw, sigv, q, r, in_idx)

Design a linear-quadratic-gaussian optimal controller for the system

          dx/dt = A x + B u + G w       [w]=N(0,[Sigw 0    ])
          y = C x + v               [v]  (    0   Sigv ])

or

          x(k+1) = A x(k) + B u(k) + G w(k)   [w]=N(0,[Sigw 0    ])
          y(k) = C x(k) + v(k)              [v]  (    0   Sigv ])

Inputs

sys

system data structure

sigw

sigv

intensities of independent Gaussian noise processes (as above)

q

r

state, control weighting respectively. Control ARE is

in_idx

names or indices of controlled inputs (see sysidx, cellidx)

default: last dim(R) inputs are assumed to be controlled inputs, all others are assumed to be noise inputs.

Outputs

k

system data structure format LQG optimal controller (Obtain A, B, C matrices with sys2ss, sys2tf, or sys2zp as appropriate).

p1

Solution of control (state feedback) algebraic Riccati equation.

q1

Solution of estimation algebraic Riccati equation.

ee

Estimator poles.

es

Controller poles.

See also: h2syn, lqe, lqr