Distributed Sequential Receding Horizon Control of Multi-Agent Systems under Recurring Signal Temporal Logic

We consider the synthesis problem of a multi-agent system under Signal Temporal Logic (STL) specifications representing bounded-time tasks that need to be satisfied recurrently over an infinite horizon. Motivated by the limited approaches to handling recurring STL systematically, we tackle the infinite-horizon control problem with a receding horizon scheme equipped with additional STL constraints that introduce minimal complexity and a backward-reachability-based terminal condition that is straightforward to construct and ensures recursive feasibility. Subsequently, assuming a separable performance index, we decompose the global receding horizon optimization problem defined at the multi-agent level into local programs at the individual-agent level the objective of which is to minimize the local cost function subject to local and joint STL constraints. We propose a scheduling policy that allows individual agents to sequentially optimize their control actions while maintaining recursive feasibility. This results in a distributed strategy that can operate online as a model predictive controller. Last, we illustrate the effectiveness of our method via a multi-agent system example assigned a surveillance task.