Control of Multi-agent Systems under STL Specifications based on Prescribed Performance Observers

This paper addresses decentralized control of large-scale heterogeneous multi-agent systems subject to bounded external disturbances and limited communication, with the objective of satisfying cooperative Signal Temporal Logic (STL) specifications. The considered specifications involve spatiotemporal tasks that require collaboration among multiple agents, including agents beyond direct communication neighborhoods. To address the communication constraints, a $k$-hop Prescribed Performance State Observer ($k$-hop PPSO) is designed to enable each agent to estimate the states of agents up to $k$ communication hops away using only information from $1$-hop neighbors, while guaranteeing predefined performance bounds on the estimation errors. The estimation error bounds are explicitly incorporated into a reformulation of the spatial robustness of the STL specifications, yielding robustness measures that account for worst-case estimation uncertainty. Based on the modified robustness, a decentralized continuous-time feedback control law is designed to guarantee satisfaction of the STL specifications in the presence of bounded disturbances and estimation errors. The proposed framework provides formal correctness guarantees using only local information and limited communication. Numerical simulations illustrate the theoretical results.