This paper primarily addresses the design of distributed optimal cooperative controllers and the utilization of a reinforcement learning (RL)-based event-triggered mechanism for multi-agent systems (MASs) with unknown dynamics. By setting an extra compensator, the augmented system is constructed to overcome the dependence for system dynamics. Then, to address the issue of computational burden, we utilize an event-triggered mechanism based on reinforcement learning (RL) and neural networks (NNs) to implement the adaptive dynamic programming (ADP) algorithm. Additionally, we take into consideration the trade-off between computational burden and achieving consensus control by introducing a weighting factor in the reward design for MASs. With this reward design, we present an algorithm based on the deep deterministic policy gradient (DDPG) algorithm to learn the event-triggered condition for MASs and achieve a balance between these two factors. The event-triggered mechanism of our algorithm can also identify constraints such as time limitations or computational resource restrictions, aiming to achieve consensus control without violating these constraints. We demonstrate the absence of Zeno behavior and the uniform ultimate boundedness (UUB) of both local consensus error and weight estimation error. Finally, simulation results illustrate the effectiveness of the control algorithm and the weighting factor.

In cyber-physical systems, the state information from multiple processes is sent simultaneously to remote estimators through wireless channels. However, with the introduction of open media such as wireless networks, cyber-physical systems may become vulnerable to denial-of-service attacks, which can pose significant security risks and challenges to the systems. To better understand the impact of denial-of-service attacks on cyber-physical systems and develop corresponding defense strategies, several research papers have explored this issue from various perspectives. However, most current works still face three limitations. First, they only study the optimal strategy from the perspective of one side (either the attacker or defender). Second, these works assume that the attacker possesses complete knowledge of the system's dynamic information. Finally, the power exerted by both the attacker and defender is assumed to be small and discrete. All these limitations are relatively strict and not suitable for practical applications. In this paper, we addressed these limitations by establishing a continuous power game problem of a denial-of-service attack in a multi-process cyber-physical system with asymmetric information. We also introduced the concept of the age of information to comprehensively characterize data freshness. To solve this problem, we employed the multi-agent deep deterministic policy gradient algorithm. Numerical experiments demonstrate that the algorithm is effective for solving the game problem and exhibits convergence in multi-agent environments, outperforming other algorithms.