Limitations for nonlinear stabilization over uncertain channels

TL;DR

This paper investigates the fundamental limits of stabilizing nonlinear systems over uncertain communication channels, highlighting the critical role of channel quality and system dynamics in achieving stabilization.

Contribution

It establishes the minimal quality of service needed for stabilization based on Lyapunov exponents, linking dynamical complexity to communication constraints.

Findings

Stabilization requires a minimal QoS related to Lyapunov exponents.

Positive Lyapunov exponents quantify the difficulty of stabilization.

Nonequilibrium dynamics influence stabilization limitations.

Abstract

We study the problem of mean-square exponential incremental stabilization of nonlinear systems over uncertain communication channels. We show the ability to stabilize a system over such channels is fundamentally limited and the channel uncertainty must provide a minimal Quality of Service (QoS) to support stabilization. The smallest QoS necessary for stabilization is shown as a function of the positive Lyapunov exponents of uncontrolled nonlinear systems. The positive Lyapunov exponent is a measure of dynamical complexity and captures the rate of exponential divergence of nearby system trajectories. One of the main highlights of our results is the role played by nonequilibrium dynamics to determine the limitation for incremental stabilization over networks with uncertainty.