Based on the Stackelberg game theory, this paper studies the optimal consensus control problem of the multi-agent system (MAS) under multiple network attacks. Multiple attackers interfere with the information interaction between agents by intervening in the transmission channel of the multi-agent wireless network, thereby changing the communication topology of the MAS. Under the limited energy of the system and attackers, the energy allocation of transmission channels is used as the performance index, and the importance of the transmission channel to the MAS is used as an auxiliary indicator to establish a Stackelberg game model between the MAS and attackers under incomplete information. By solving the Stackelberg equilibrium solution of the game model, the optimal attack energy allocation scheme and the optimal energy allocation scheme of the system are obtained, respectively. Then, based on the equilibrium solution, the Hamilton-Jacobi-Bellman equation with coupling terms for the MAS under attacks is given. In view of the broad learning system theory, online algorithms that approximate the optimal performance function and the optimal controller are designed respectively, and sufficient conditions are obtained for the proposed optimal controller to ensure the stability and consistency of the MAS. Finally, the effectiveness of the method is verified by a numerical simulation.

With the rapid development of artificial intelligence technology and Internet of Things technology, cyber–physical systems (CPSs) have also been fully developed, which promotes the widespread use of CPS in a variety of areas and brings many new opportunities and challenges. This article considers the consistent identification of finite impulse response (FIR) systems with multilevel quantized observations subjected to data tampering attacks. First, a defense algorithm based on known parameters is designed for the case where the attack is known. Second, on the basis of the algorithm with known attack, a joint consistent estimation approach is proposed for estimating system parameters, and the convergence and asymptotic normality of the algorithm are proved. Then, according to the asymptotic normality of the algorithm, the trace of the defense algorithm’s asymptotic error covariance matrix is used as the defense index to establish the optimal defense model. Finally, the effectiveness of the defense strategy is verified through experiments.

This brief designs a distributed stochastic annealing algorithm for nonconvex cooperative aggregative games, whose players’ cost functions not only depend on players’ own decision variables but also rely on the sum of players’ decision variables. To seek the social optimum of cooperative aggregative games, a distributed stochastic annealing algorithm is proposed, where the local cost functions are nonconvex and the communication topology between players is time-varying. The weak convergence to the social optimum of the algorithm is further analyzed. A numerical example is finally given to illustrate the effectiveness of the proposed algorithm.