Improvability of Feedback Systems

This paper introduces the notion of improvability and bottlenecks of feedback systems in the context of instrumentation cost. Specifically, a feedback system is improvable if its performance can be enhanced by re-allocating sensor and actuator costs under budget constraints. We derive a criterion which determines when the system is improvable, using the LQG performance index. In addition, we introduce and analyze the notion of instrumentation bottleneck and provide a criterion for bottleneck identification. An important feature of the results derived is that both improvability and BN indicators can be evaluated using on-line measurements in the feedback loop, without requiring precise knowledge of the plant data. Examples illustrating results are provided.