Probabilistic Tube-based Control Synthesis of Stochastic Multi-Agent Systems under Signal Temporal Logic

TL;DR

This paper introduces a probabilistic tube-based control synthesis method for stochastic multi-agent systems that ensures STL specifications are satisfied with a predefined probability, reducing conservatism and enabling scalable solutions.

Contribution

It presents a novel probabilistic reachable tube approach and a recursive algorithm for multi-agent control synthesis under STL constraints, improving scalability and robustness.

Findings

Successfully applied to a ten-agent system.

Reduces conservatism compared to existing methods.

Enables scalable control synthesis for stochastic multi-agent systems.

Abstract

We consider the control design of stochastic discrete-time linear multi-agent systems (MASs) under a global signal temporal logic (STL) specification to be satisfied at a predefined probability. By decomposing the dynamics into deterministic and error components, we construct a probabilistic reachable tube (PRT) as the Cartesian product of reachable sets of the individual error systems driven by disturbances lying in confidence regions (CRs) with a fixed probability. By bounding the PRT probability with the specification probability, we tighten all state constraints induced by the STL specification by solving tractable optimization problems over segments of the PRT, and relax the underlying stochastic problem with a deterministic one. This approach reduces conservatism compared to tightening guided by the STL structure. Additionally, we propose a recursively feasible algorithm to attack the resulting problem by decomposing it into agent-level subproblems, which are solved iteratively according to a scheduling policy. We demonstrate our method on a ten-agent system, where existing approaches are impractical.