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This work addresses the problem of learning optimal control policies for a multi-agent system in an adversarial environment. Specifically, we focus on multi-agent systems where the mission objectives are expressed as signal temporal logic (STL) specifications. The agents are classified as either defensive or adversarial. The defensive agents are maximizers, namely, they maximize an objective function that enforces the STL specification; the adversarial agents, on the other hand, are minimizers. The interaction among the agents is modeled as a finite-state team stochastic game with an unknown transition probability function. The synthesis objective is to determine optimal control policies for the defensive agents that implement the STL specification against the best responses of the adversarial agents. A multi-agent deep Q-learning algorithm, which is an extension of the minimax Q-learning algorithm, is then proposed to learn the optimal policies. The effectiveness of the proposed approach is illustrated through a simulation case study. 

This paper presents a Q-Iearning based dynamic intermittent mechanism to control linear systems evolving in continuous time. In contrast to existing event-triggered mechanisms, where complete knowledge of the system dynamics is required, the proposed dynamic intermittent control obviates this requirement while providing a quantified level of performance. An internal dynamical system will be introduced to generate the triggering condition. Then, a dynamic intermittent Q-Iearning is developed to learn the optimal value function and the hybrid controller. A qualitative performance analysis of the dynamic event-triggered control is given in comparison to the continuous-triggered control law to show the degree of suboptimality. The combined closed-loop system is written as an impulsive system, and it is proved to have an asymptotically stable equilibrium point without any Zeno behavior. A numerical simulation of an unknown unstable system is presented to show the efficacy of the proposed approach.