Control system design subject to SNR constraints

Abstract

This paper deals with networked control systems comprising LTI plants controlled over scalar additive noise channels subject to signal-to-noise ratio (SNR) constraints. We present a general framework, based upon convex optimization concepts, that can accommodate several situations of interest. Our results make explicit the fact that feedback around the channel plays a key role in reducing the minimal SNR that is compatible with stability. The results also provide a characterization of the best achievable performance subject to an SNR constraint. We apply the results to specific networked control architectures, and provide a numerical example.

A Framework for Control System Design Subject to Average Data-Rate Constraints

“…We see from Corollary 6.1 that the study of conditions on γ for MSS are insufficient to give performance guarantees. This fact is unsurprising, and consistent with results in [15], [51].…”

“…Our results thus establish a formal relationship between SNR constraints and average data-rates constraints in noiseless digital channels. As such, our work goes beyond [6], [51] where no such relationship is presented. Early versions of the results reported in the paper can be found in [47], [50].…”

“…A key enabling result in the paper is that, when the proposed class of source-coding schemes is employed, average data-rate constraints can be enforced by imposing signal-to-noise ratio (SNR) constraints in a related analog additive noise channel (see also [6], [51]). Our results thus establish a formal relationship between SNR constraints and average data-rates constraints in noiseless digital channels.…”

Optimal tracking performance of discrete-time systems with quantization

“…For instance, in [18], SNR fundamental limitations are investigated for discrete-time single-input and single-output (SISO) NCSs. A tight condition of communication SNR is obtained for the linear time invariant output feedback stabilization of a discrete-time.…”

“…The most problems under consideration focus on how to model the networked control system and stabilization analysis with quantization effects [9,16,22], time delays [9,13,14,28], bandwidth constraint [5,6,19], and signal-to-noise ratio (SNR) constraint [4,7,17,18] over the communication channels. These studies investigate mostly the problem of stability analysis and stabilization for networked control systems.…”