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This paper addresses the challenge of synthesizing safe controllers for discrete-time linear multi-agent systems with limited k-hop communication by developing a distributed observer that reconstructs remote states and provides a uniform error bound. The approach integrates this observer-induced perturbation into the design of local $\epsilon_i$-robust safe invariant (RSI) sets and pairwise relative-state safety constraints to guarantee closed-loop safety. A linear matrix inequality (LMI)-based optimization framework is then employed to jointly synthesize the distributed observers, local controllers, and RSI sets, demonstrating effectiveness in a case study.
A single LMI optimization framework unifies distributed k-hop observer design with robust safe controller synthesis for linear multi-agent systems, overcoming the state estimation-controller coupling challenge.
This paper studies communication-aware safe control for discrete-time linear multi-agent systems under limited information exchange. The main challenge lies in the coupling between remote-state estimation and safe controller design, since estimation errors affect the state evolution through the controller gains, while the controller design must account for the resulting observer-induced state perturbations to guarantee safety. To address this challenge, a distributed k-hop observer is developed to reconstruct unavailable remote states, and a uniform observer-error bound is derived. The effect of the observer-induced state perturbation on closed-loop safety is accounted for in both the construction of local {\epsilon}i-robust safe invariant (RSI) sets and the enforcement of pairwise relative-state safety constraints. The resulting safety conditions ensure that all agents remain within their local RSI sets while all pairwise relative-state safety constraints are satisfied. A linear matrix inequality (LMI)-based optimization method is developed to jointly synthesize the distributed observers, local controllers, and RSI sets. A case study illustrates the effectiveness of the proposed method.
