Steady-state optimal controller with actuator noise variance linearly related to actuator signal variance

The linear-quadratic-Gaussian (LQG) method assumes that the covariance matrix of the actuator noise is given before the design of the feedback matrix. However, in practice, the actuator-noise covariance matrix may depend on the actuator signal energy, which depends on the feedback. Consequently, the feedback from LQG theory degrades the system performance. The authors investigate the steady-state optimal controller when the noise variance of an actuator is linearly related to the variance of an actuator signal. This control system could be much more precise and/or spend much less control energy than the one obtained through the use of the ordinary LQG method