Improvability of feedback systems with saturating actuators and noisy sensors

A feedback system is called improvable under budget constraints if its performance can be enhanced by re-allocating instrumentation cost between sensors and actuators. An instrument (i.e., sensor or actuator) is called the bottleneck of a feedback system if its improvement leads to the largest improvement of the system performance index. In this paper, these concepts are applied to SISO feedback systems with saturating actuators and noisy sensors. The approach is based on a recently developed extension of the LQG theory to systems with saturating actuators. Using this theory and assuming that more expensive actuators and sensors ensure less saturation and measurement noise, respectively, we derive an improvability and bottleneck indicator, which determines when and how the system can be improved. Illustrating examples are provided.