Collaborative Safety-Critical Control for Dynamically Coupled Networked Systems

TL;DR

The paper addresses safety in dynamically coupled networked systems by defining collaborative control barrier functions ($CCBF$) and a decentralized safety algorithm that accounts for 1-hop neighborhood dynamics to enforce forward invariance of node-level safe sets. It develops a rigorous formulation using high-order barrier concepts and a round-based collaboration protocol that negotiates safety responsibilities among neighbors, proving convergence under weakly non-interfering constraints. The approach yields a viable, safety-guaranteeing control action for each node while remaining close to nominal policies, demonstrated on a networked SIS epidemic model where cooperation among nodes is essential for maintaining safety. This work offers scalable safety guarantees for interconnected systems and points to future extensions to multi-hop coupling and edge-control in network dynamics, with practical relevance to infrastructure and epidemiological networks.

Abstract

As modern systems become ever more connected with complex dynamic coupling relationships, developing safe control methods becomes paramount. In this paper, we discuss the relationship of node-level safety definitions for individual agents with local neighborhood dynamics. We define a collaborative control barrier function (CCBF) and provide conditions under which sets defined by these functions will be forward invariant. We use collaborative node-level control barrier functions to construct a novel \edit{decentralized} algorithm for the safe control of collaborating network agents and provide conditions under which the algorithm is guaranteed to converge to a viable set of safe control actions for all agents. We illustrate these results on a networked susceptible-infected-susceptible (SIS) model.

Figures (2)

• Figure 1: An example of when node $i \in [n]$ is constrained by two neighbors, where $u_i \in \mathbb{R}^2$. The constrained control space for agent $i$, $\mathcal{U}_i$, is shaded green, with the feasibly safe control actions for neighbors 1 and 2 shaded in blue and red, respectively. Both $\overline{\mathcal{U}}_{1i}$ and $\overline{\mathcal{U}}_{2i}$ are individually feasible, but jointly infeasible, with the set of feasible, safe control actions for neighbors 1 and 2 shown in the purple-shaded region. The compromise-seeking action $\overline{u}_i \in \mathbb{R}^2$ is marked on the boundary of $\mathcal{U}_i$, which is the closest action in $\mathcal{U}_i$ to the feasible, safe control actions for both neighbors $\overline{\mathcal{U}}_{1i} \cap \overline{\mathcal{U}}_{2i}$. The set of all viable compromise-seeking actions $\overline{\partial \mathcal{U}}_i$ is shown by the yellow line and the current set of compromise-seeking actions $\overline{\partial \mathcal{U}}_i^\tau$ is shown by the pink line.
• Figure 2: Simulated collaborative decentralized controllers for a networked SIS model with $n=3$ where dotted lines represent each node's safety constraints $\bar{x}_i$ and the black dashed line showing the input constraint of $\mathcal{U}_i = [0, 0.75]$ for all nodes $i \in [n]$, respectively.

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Definition 3
• Lemma 1
• Definition 4
• Theorem 1
• proof
• Definition 5
• Lemma 2
• proof