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In this paper, we study the cooperative optimization problem (COP) for fuzzy nonlinear multi-agent systems (MASs) subjecting to denial-of-service (DoS) attacks. Unlike the existing cooperative optimization results, both fuzzy nonlinear systems and DoS attacks are considered in this paper. To solve the problem, a hierarchical equivalence mechanism is first introduced to transform the COP into an equivalent one consisting of both a distributed optimization problem (DOP) and a decentralized tracking problem (DTP). By introducing an optimal distributed algorithm, a customized virtual signal is devised to minimize the optimization function and simultaneously mitigate the effects of DoS attacks. To construct a bridge between solving the COP and the DTP, a local reference generator, which includes the characteristics of existing high-order derivatives, is designed utilizing the Hermite interpolation method. Subsequently, the backstepping technique is employed to create a decentralized fuzzy adaptive controller. It is illustrated that the proposed method is capable of achieving the cooperative optimization objective. Finally, the theoretical results are successfully applied to show the efficiency of the proposed method.
Fan et al. (Mon,) studied this question.