Neural‐network‐based control for discrete‐time nonlinear systems with denial‐of‐service attack: The adaptive event‐triggered case

This article investigates a neural network (NN)‐based control problem for unknown discrete‐time nonlinear systems with a denial‐of‐service (DoS) attack and an adaptive event‐triggered mechanism (ETM). The considered DoS attacks are described by the occurrence frequency and durations and hence more general in comparison with existing stochastic models. To the addressed problem, a novel adaptive rule adjusting the triggering threshold of ETM is constructed to govern the communication schedule, and an NN‐based observer is designed to identify the system dynamics where a piecewise update rule of NN weights is adopted to handle the challenge of the complex time series coming from both ETM and DoS attacks. In light of this kind of protocol‐ and attack‐induced switched systems, a sufficient condition dependent on the occurrence frequency and durations of DoS attacks is elaborately established via the analysis of input‐to‐state stability. Furthermore, an iteration adaptive dynamic programming approach is proposed to handle the addressed control issue, and the boundedness is discussed to both the estimation errors of the Luenberger‐type observer and the identified errors of NN weights of observer networks as well as actor‐critic networks with the help of the Lyapunov theory. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.