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

TL;DR

This paper develops a decentralized control framework for large multi-agent systems to satisfy spatiotemporal STL specifications despite disturbances and limited communication, using a novel $k$-hop PPSO for state estimation.

Contribution

It introduces a $k$-hop Prescribed Performance State Observer enabling agents to estimate distant states with performance guarantees, integrating this into STL robustness for decentralized control.

Findings

The $k$-hop PPSO guarantees predefined estimation error bounds.

The control law ensures STL specification satisfaction under disturbances and estimation errors.

Simulations validate the effectiveness of the proposed approach.

Abstract

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.