Feedback stabilization over signal-to-noise ratio constrained channels

Abstract

There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signal-to-noise ratio (SNR) constraints are one way in which data-rate limits arise, and are the focus of this paper. In both continuous and discrete-time settings, we show that there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finite-dimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delay-free, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuous-time nonminimum phase plant, a periodic linear time varying feedback scheme with fast sampling may be used to recover the original SNR requirement at the cost of robustness properties. The proposed framework inherently captures channel noise effects in a simple formulation suited to conventional LTI control performance and robustness analysis, and has potential to handle time delays and bandwidth constraints in a variety of control over communication links problems.

Stabilization and Entropy Reduction via SDP-Based Design of Fixed-Order Output Feedback Controllers and Tuning Parameters

“…The polynomials r i (v) have degree in the range [4,6], the number of LMI scalar variables is 262, and the computational time is less than 1 second.…”

“…Hence, we make Change C3 in (65)-(66) and we solve the SDP (67) with d = 2. The polynomials r i (v) have degree in the range [2,4], the number of LMI scalar variables is 332, and the computational time is less than 2 seconds. At this point, we look for v * ∈ R 3 satisfying the fourth constraint in (59).…”

“…The EM is important because allows one to establish whether a stabilizing controller can be designed in a number of scenarios characterized by the presence of communication constraints. Indeed, this is shown in the contexts of quantized feedback stabilization [12], data rate constrained mean square stabilizability [21], data rate constrained observability and stabilizability [27], stabilization with sector bound uncertainty [13], signal-to-noise ratio (SNR) constrained feedback stabilization [4], and stabilization with multirate sampling [5]. See Section II-B for details, and see also [18], [20] for other applications of the EM.…”

Robust Stability Analysis and Synthesis for Uncertain Discrete-Time Networked Control Systems Over Fading Channels

“…Considering different information constraints, numerous methods have been proposed by researchers for analysis and synthesis. Among the methods, one should mention [2], [3] which deal with quantized feedback control, [4], [5] which investigate the time delay, [6], [7] where constraints on the signal-to-noise ratio are considered, and [8], [9] where the problem of resource allocation is addressed. On the other hand, as it often happens when dealing with real systems, the model of the plant is partially or completely unknown, which leads to a further research problem, networked control of uncertain systems.…”

Output Feedback Stabilization for Discrete-Time Systems Under Limited Communication

“…Last but not least, most of the control design efforts so far, e.g. [11], [18], [22]- [24], are devoted to channel features and, due to the fact that the controller minimizing the H ∞ (H 2 ) norm of the sensitivity (complimentary sensitivity) is the one adopted in the existing work, there has been no space left for consideration of system performance. These facts motivate our current research.…”