Observer-based Control of Multi-agent Systems under STL Specifications

This paper proposes a decentralized controller for large-scale heterogeneous multi-agent systems subject to bounded external disturbances, where agents must satisfy Signal Temporal Logic (STL) specifications requiring cooperation among non-communicating agents. To address the lack of direct communication, we employ a decentralized k-hop Prescribed Performance State Observer (k-hop PPSO) to provide each agent with state estimates of those agents it cannot communicate with. By leveraging the performance bounds on the state estimation errors guaranteed by the k-hop PPSO, we first modify the space robustness of the STL tasks to account for these errors, and then exploit the modified robustness to design a decentralized continuous-time feedback controller that ensures satisfaction of the STL tasks even under worst-case estimation errors. A simulation result is provided to validate the proposed framework.

💡 Research Summary

The paper addresses the challenging problem of guaranteeing that a large‑scale heterogeneous multi‑agent system (MAS) satisfies global Signal Temporal Logic (STL) specifications even when many agents that must cooperate cannot directly communicate. The authors propose a fully decentralized solution that combines a novel k‑hop Prescribed Performance State Observer (k‑hop PPSO) with a modified robustness‑based controller.

First, each agent runs a k‑hop PPSO that exploits the network’s communication graph to estimate the states of agents up to k hops away, where k is chosen to cover every task‑dependency that lacks a direct communication link. The observer is designed with prescribed performance functions δ(t) and ρ(t) that bound the estimation error |˜xᵢʳ(t)| < δᵢʳ(t) for every estimated neighbor r. This guarantee holds uniformly for all trajectories, provided the agents’ dynamics are locally Lipschitz, the input matrix is uniformly positive‑definite, and the external disturbances are bounded. The observer dynamics employ a logarithmic transformation and a nonlinear feedback term that forces the error to decay within the prescribed envelope, extending earlier single‑hop observer designs to arbitrary hop distances while preserving scalability.

Second, the authors recognize that STL satisfaction is traditionally expressed through the space robustness function ρψ(x). Because the controller will only have access to the estimated state vector ˆx, they derive a worst‑case robustness correction εᵢ(t) based on the known error bounds from the PPSO. The corrected condition becomes ρψᵢ(ˆx) ≥ ρψᵢ(x) − εᵢ(t), ensuring that if the corrected robustness stays above a time‑varying lower bound, the original STL formula is guaranteed to hold despite estimation errors.

Third, a decentralized Prescribed Performance Controller (PPC) is synthesized for each agent. The controller uses a smooth approximation of the min‑operator (log‑sum‑exp) to obtain a differentiable robustness surrogate, then applies a feedback law of the form
uᵢ = gᵢ⁻¹(xᵢ)