Distributed State Estimation with Deep Neural Networks for Uncertain Nonlinear Systems under Event-Triggered Communication

This work explores the distributed state estimation problem for an uncertain, nonlinear, and continuous-time system. Given a sensor network, each agent is assigned a deep neural network (DNN) which is used to approximate the system's dynamics. Each agent updates the weights of their DNN through a multiple timescale approach, i.e., the outer layer weights are updated online with a Lyapunov-based gradient descent update law, and the inner layer weights are updated concurrently using a supervised learning strategy. To promote the efficient use of network resources, the distributed observer uses event-triggered communication. A nonsmooth Lyapunov analysis demonstrates that the distributed event-triggered observer achieves uniformly ultimately bounded state reconstruction. A simulation example of a 5-agent sensor network estimating the state of a two-link robotic manipulator tracking a desired trajectory is provided to validate the result and showcase the performance improvements afforded by DNNs.