Can Decentralized Control Outperform Centralized? The Role of Communication Latency

TL;DR

This paper investigates how communication latency that scales with network connectivity impacts the performance of distributed versus centralized control in networks of $N$ agents. By analyzing continuous-time and discrete-time models with single- and double-integrator dynamics on undirected graphs, the authors decompose steady-state performance into a network-architecture term and a latency term, revealing a fundamental trade-off: as the number of communication links increases, latency grows and can negate the benefits of denser connectivity. Through both analytical results on ring topologies and numerical experiments on general symmetric topologies, they show that under sufficiently latency-increasing topologies, sparse, nearest-neighbor controllers can outperform fully connected centralized controllers. The study provides convex formulations for single-integrator designs and time-scale separation-based approximations for double-integrator designs, offering practical guidance for designing scalable, latency-aware distributed controllers. These insights have implications for large-scale wireless networks where bandwidth constraints make latency a key performance limiter.

Abstract

In this paper, we examine the influence of communication latency on performance of networked control systems. Even though distributed control architectures offer advantages in terms of communication, maintenance costs, and scalability, it is an open question how communication latency that varies with network topology influences closed-loop performance. For networks in which delays increase with the number of links, we establish the existence of a fundamental performance trade-off that arises from control architecture. In particular, we utilize consensus dynamics with single- and double-integrator agents to show that, if delays increase fast enough, a sparse controller with nearest neighbor interactions can outperform the centralized one with all-to-all communication topology.

Figures (8)

• Figure 1: Steady-state variance $J_{\textrm{tot}}(n)$ versus number of neighbors. The variance is the sum of two costs: $J_{\textrm{network}}(n)$ represents impact of control architecture, while ${J}_{\textrm{latency}}(n)$ is due to the delays affecting the dynamics.
• Figure 2: Level curves of the steady-state variance for the continuous-time double integrator \ref{['eq:agent-dynamics-1']} and points of minimum with fixed derivative gain.
• Figure 3: Exact variance function \ref{['eq:cont-time-single-int-steady-state-variance']} and its quadratic approximation.
• Figure 4: Optimal and suboptimal steady-state scalar variances with linear delay increase for different agent dynamics.
• Figure 5: Network topology and its optimal closed-loop variance.

Theorems & Definitions (15)

• Remark 1: Architecture parametrization
• Proposition 1: Stability of CT single integrators
• proof : Sketch of Proof
• Corollary 1
• proof
• Proposition 2: Stability of CT double integrators
• proof
• Remark 2: Non-normalized delay
• Proposition 3: Near-optimal proportional control
• proof