lqg (Robust Control Toolbox)

LQG optimal control synthesis.

[af,bf,cf,df] = lqg(A,B,C,D,W,V) 
[ssf] = lqg(ss,w,v)

Description
lqg computes an optimal computes an optimal controller to stabilize the plant G(s)

and minimize the quadratic cost function

Figure 1-12: LQG Synthesis.

The plant noise

and measurement noise

are white and Gaussian with joint correlation function

The input variables W and V are

The LQG controller is returned as F(s) := (af, bf, cf, df).

Algorithm
The solution of the LQG problem is a combination of the solutions of Kalman filtering and full-state feedback problems based on the so-called separation principle. The individual problems are explained under lqe and lqr in the Control System Toolbox. The final negative-feedback controller has the form (e.g. [1])

Note that the sign of

is minus that in the function h2lqg; this is because by convention lqg feedback is negative (i.e,

) while the h2lqg is positive (i.e,

). The lqg feedback can also be realized as a full-state feedback and Kalman filter:

See Also
h2lqg, hinf, hinfdemo, linf, linfdemo, ltru, ltry

References
[1] M. Athans, "The Role and Use of the Stochastic Linear-Quadratic-Gaussian Problem in Control System Design," IEEE Trans. Automat. Contr., AC-16, pp. 529-552, Dec. 1971.

lftf ltru, ltry