Feedback Systems with Communications: Integrated Study of Signal Estimation, Sampling, Quantization, and Feedback Robustness

Feedback systems with communication channels encounter unique challenges. Communication channels mandate signal sampling and quantization, and introduce errors, data losses, and delays. Consequently, transmitted signals must be estimated. The signal estimation introduces a dynamic system that interacts with communication channels and affects the stability and performance of the feedback system. This paper studies interactions among communications, sampling, quantization, signal estimation, and feedback, in terms of fundamental stability and performance limitations. Typical empirical-measure-based algorithms are used for signal estimation under quantized observations. When the sampling interval and signal estimation step size are coordinated, the ODE approach for stochastic approximations provides a suitable platform for an integrated system analysis for signal estimation, sampling and quantization, and feedback robustness. Feedback design for enhancing robustness against communication uncertainty and signal estimation dynamics is studied under the new notion of stability margin under signal averaging. Fundamental limitations on noise attenuation in such an integrated system are derived.