  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, we decompose the
global receding horizon optimization problem into agent-level programs the
objectives of which are to minimize local cost functions 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.
