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This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak–Łojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.

The neural network-based adaptive backstepping method is an effective tool to solve the cooperative tracking problem for nonlinear multiagent systems (MASs). However, this method cannot be directly extended to the case without continuous communication. It is because the discontinuous communication results in discontinuous signals in this case, the standard backstepping method is inapplicable. To solve this problem, a hierarchical design scheme that involves distributed cooperative estimators and neural network-based decentralized tracking controllers is proposed. By introducing a dynamic event-triggered mechanism, cooperative intermediate parameter estimators are first designed to estimate the unknown parameters of the leader. By using the interpolation polynomial method, these estimators are extended to smooth estimators with high-order derivatives to guarantee that the backstepping method is applicable. Based on the state of the smooth estimators, a backstepping-based decentralized neural network tracking controller is designed. It is shown that the tracking errors are asymptotically convergent and all the signals in the closed-loop systems are bounded. Compared with the existing cooperative tracking results for nonlinear MASs with event-triggered communication, a more general class of MASs is considered in this article and a better performance in terms of asymptotic tracking is achieved. Finally, a simulation example is given to show the effectiveness of our developed method.

The problem of the model-free adaptive resilient control (MFARC) for nonlinear cyber–physical systems (CPSs) suffered from aperiodic jamming attacks is investigated in this article. First, the MFARC framework subject to aperiodic jamming attacks is established, and an intermediate variable method is introduced to avoid using the unavailable time-varying parameter and further eliminate an extra assumption on the sign limit of it. Then, a MFARC scheme is devised to track the desired output, where the problem of the tracking control can be transformed into solving a feasibility problem, and the controller parameters can be obtained with the aid of the linear matrix inequality technique. What is more, a novel attack compensation mechanism is developed in the MFARC scheme to mitigate the impact of aperiodic jamming attacks. In the last, an example is provided to verify the effectiveness of the devised MFARC scheme.