Neural-Network-Based Secure State Estimation Under Energy-Constrained Denial-of-Service Attacks: An Encoding-Decoding Scheme

This paper is concerned with the secure state estimation issue for a class of networked nonlinear systems under energy-constrained denial-of-service (EC-DoS) cyber-attacks and encoding-decoding scheme (EDS). The information transmissions between sensors and the estimator are executed via a bandwidth-limited communication network, on which the EDS is deployed to convert transmitted signals into finite-length codewords for the purpose of improving transmission efficiency. The EC-DoS attacks, whose intention is to jeopardize the network-based signal transmissions by overloading the communication resource, are assumed to occur in an intermittent way with bounded occurrence frequency/durations owing to the inherent energy constraints on the attackers. Considering the worst case of such EC-DoS attacks, a neural-network (NN)-based state estimator is constructed to generate the desired state estimates for the underlying networked nonlinear system. By employing the Lyapunov stability theory, the estimation error dynamics of the system state and the neural-network weight are jointly analyzed within a unified framework. Subsequently, sufficient conditions are obtained for the existence of the desired NN-based state estimator, and then both the desired estimator gain matrix and the NN tuning parameters are characterized. Finally, the validity of our estimation approach is confirmed by an example.