On a notion of estimation entropy for stochastic hybrid systems

Abstract

The advent of emerging fields such as networked control systems and wireless sensor networks involving information flow over bandwidth-constrained digital channels has presented the control and information theory communities with a new set of challenges. One of these challenges is to accurately estimate the trajectory of (stochastic) nonlinear systems using sampled and quantized state measurements transmitted over a finite-bandwidth digital channel. This has led researchers to study these problems by combining notions from both control and communication domains, two fields which have been traditionally treated separately. A recent notion introduced in this context is called estimation entropy, which has been defined as the minimum bit rate required to estimate the trajectory of a deterministic nonlinear system with a given exponential convergence rate. In this paper, we show that this notion can be extended to continuous-time stochastic systems as well, particularly, a class of stochastic hybrid systems. We also provide an upper bound on the estimation entropy for this class of systems.