RNN-Based Learning of Nonlinear Dynamic System Using Wireless IIoT Networks

Abstract

We consider the recurrent neural network (RNN)-based remote state estimation for nonlinear dynamic systems with unknown state dynamics. The nonlinear dynamic plant is monitored by multiple distributed IIoT sensors over a random access wireless network with shared common spectrum. We focus on the remote state estimation algorithm design so as to achieve remote state estimation stability subject to noninvertible nonlinear sensor state observations, imperfect channel state information (CSI) at the remote estimator, and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. Utilizing a state diffeomorphism, the original system is transformed into a canonical form with a linear rank deficient observation matrix. We propose a novel RNN remote state estimator based on the pole placement design associated with the transformed rank deficient state measurement matrices. We further propose a novel online training algorithm such that the RNN at the remote estimator can not only address the divergence issue over wireless networks but also effectively learn the unknown nonlinear plant dynamics despite rank deficiency and imperfect CSI. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in the high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearity can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.