Remote State Estimation of Nonlinear Systems Over Fading Channels via Recurrent Neural Networks

In this article, we consider the remote state estimation for nonlinear dynamic systems with known linear dynamics and unknown nonlinear perturbations. The nonlinear dynamic plant is monitored by multiple distributed sensors over a random access wireless network with shared common radio channel. We focus on the communication strategy and remote state estimation algorithm design so as to achieve a remote state estimation stability subject to unknown nonlinearities in plant and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. By exploiting the additive properties of the physical wireless channels, we propose a novel information fusion over-the-air mechanism to address the signal collision and interference among the sensors. Utilizing the partial knowledge on the linear dynamics of the plant, we also propose a novel recurrent neural network (RNN)-based remote state estimator aided by a virtual state estimation mean-square-error (MSE) process. We further propose a novel online training algorithm such that the RNN at the remote estimator can effectively learn the unknown plant nonlinearities. 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 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 nonlinearities 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.