Finding optimal adversarial attack strategies is an important topic in reinforcement learning and the Markov decision process. Previous studies usually assume one all-knowing coordinator (attacker) for whom attacking different recipient (victim) agents incurs uniform costs. However, in reality, instead of using one limitless central attacker, the attacks often need to be performed by distributed attack agents. We formulate the problem of performing optimal adversarial agent-to-agent attacks using distributed attack agents, in which we impose distinct cost constraints on each different attacker-victim pair. We propose an optimal method integrating within-step static constrained attack-resource allocation optimization and between-step dynamic programming to achieve the optimal adversarial attack in a multi-agent system. Our numerical results show that the proposed attacks can significantly reduce the rewards received by the attacked agents.

It poses technical difficulty to achieve stable tracking even for single mismatched nonlinear strict-feedback systems when intermittent state feedback is utilized. The underlying problem becomes even more complicated if such systems are networked with directed communication and state-triggering setting. In this work, we present a fully distributed neuroadaptive tracking control scheme for multiple agent systems in strict-feedback form using triggered state from the agent itself and the triggered states from the neighbor agents. To circumvent the non-differentiability of virtual controllers stemming from state-triggering, we first develop a distributed continuous control scheme under regular state feedback, upon which we construct the distributed event-triggered control scheme by replacing the states in the preceding scheme with the triggered ones. Several useful lemmas are introduced to allow the stability condition to be established with such replacement, ensuring that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with the output tracking error converging to a residual set around zero. Besides, with proper choices of the design parameters, the tracking performance in the mean square sense can be improved. Numerical simulation verifies the benefits and efficiency of the proposed method.