Deep learning of a communication policy for an event-triggered observer for nonlinear systems

Abstract

This paper examines the problem of designing an event-triggered observer for discrete-time nonlinear systems by learning an optimal communication policy based on available input and output data. An emulation strategy is followed, wherein the observer is initially designed assuming full knowledge of the plant output at any instant. Then, communication constraints are taken into account and the objective is to construct an optimal transmission policy to minimize the amount of data exchanges between the sensors and the observer while preserving the convergence properties of the latter. First, our goal is to design the communication policy to minimize an infinite horizon discounted cost whose stage cost penalizes both the state estimation error and the number of events. The existence of such an optimal policy is guaranteed under mild conditions on the initially designed observer. Moreover, optimal policy are shown to preserve the desired convergence property of the observer. This optimization problem can be formulated as a mixed-integer nonlinear program, which is challenging to solve exactly. To address this, a deep learning algorithm is proposed to approximate the solution using recurrent neural networks. Finally, simulation examples demonstrate the effectiveness and robustness of the learned communication policies.