  Decentralized multi-agent control has broad applications, ranging from
multi-robot cooperation to distributed sensor networks. In decentralized
multi-agent control, systems are complex with unknown or highly uncertain
dynamics, where traditional model-based control methods can hardly be applied.
Compared with model-based control in control theory, deep reinforcement
learning (DRL) is promising to learn the controller/policy from data without
the knowing system dynamics. However, to directly apply DRL to decentralized
multi-agent control is challenging, as interactions among agents make the
learning environment non-stationary. More importantly, the existing multi-agent
reinforcement learning (MARL) algorithms cannot ensure the closed-loop
stability of a multi-agent system from a control-theoretic perspective, so the
learned control polices are highly possible to generate abnormal or dangerous
behaviors in real applications. Hence, without stability guarantee, the
application of the existing MARL algorithms to real multi-agent systems is of
great concern, e.g., UAVs, robots, and power systems, etc. In this paper, we
aim to propose a new MARL algorithm for decentralized multi-agent control with
a stability guarantee. The new MARL algorithm, termed as a multi-agent
soft-actor critic (MASAC), is proposed under the well-known framework of
"centralized-training-with-decentralized-execution". The closed-loop stability
is guaranteed by the introduction of a stability constraint during the policy
improvement in our MASAC algorithm. The stability constraint is designed based
on Lyapunov's method in control theory. To demonstrate the effectiveness, we
present a multi-agent navigation example to show the efficiency of the proposed
MASAC algorithm.
