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

Integrating instrumentation and control design

“…Ruan and Choudhury (1993) and Krolikowski (1997) studied the LQG control problem for a ® rst-order system (the state is a scalar) where the actuator noise variance is linearly related to the actuator signal variance. Skelton (1994) was the ® rst to introduce the ® nite signal-to-noise model for general linear systems.…”

Exact Analytic Solutions for Optimal Control Problems Under Multiplicative Noise*

“…Often, such signal dependent noise has significant effects in control systems such as aerospace thrust control, digital feedback control, chemical reactors, analog mechanical actuators, biological muscles, and synaptic transmission of neural systems (see McLane [1971], Ibrahim [1985], van Wingerden and De Koning [1984], Wagenaar [1989], Bolotin [1984], Ruan and Choudhury [1993] and Harris and Wolpert [1998]). In these models, noise is often modeled as being amplified by the control signal in a multiplicative manner.…”

“…Most control problems with multiplicative noise have been anlayzed on the basis of linear control model with quadratic cost functions on state and control signals (see Wonham [1967], Willems and Willems [1976], Phillis [1985], Kubrusly and Costa [1985], Ruan and Choudhury [1993], Yaz and Skelton [1994], Boyd et al [1994], El Ghaoui [1995], Lu and Skelton [2000], Todorov [2005]). …”

State estimation with finite signal-to-noise models

“…One important benefit of the FSN model in a linear control problem is that it keeps the control finite at the maximal accuracy [7]. This is in contrast to LQG theory, where the maximal accuracy occurs at infinite control.…”