Optimal Data Rate for State Estimation of Switched Nonlinear Systems

Abstract

State estimation is a fundamental problem for monitoring and controlling systems. Engineering systems interconnect sensing and computing devices over a shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. We present a notion of entropy for state estimation of switched nonlinear dynamical systems, an upper bound for it and a state estimation algorithm for the case when the switching signal is unobservable. Our approach relies on the notion of topological entropy and uses techniques from the theory for control under limited information. We show that the average bit rate used is optimal in the sense that, the efficiency gap of the algorithm is within an additive constant of the gap between estimation entropy of the system and its known upper-bound. We apply the algorithm to two system models and discuss the performance implications of the number of tracked modes.

Comprehending Complexity: Data-Rate Constraints in Large-Scale Networks

“…Description of the input-to-output properties addresses the incremental values of the input and output of the linearized system (16), and is stated in the following.…”

Observing a Unicycle Robot with Data Rate Constraints: a Case Study

“…For nonlinear systems, early important results include [21] and [15], which use the concept of entropy to characterize the minimum data rates. Many more papers exploited entropy-based techniques to provide constructive bounds on the sufficient/necessary data rates (see [12], [19], [13], [23], [16], [17], [24], [28] and [18]).…”

Observation of nonlinear systems via finite capacity channels, Part II: Restoration entropy and its estimates

“…As is now known, the issue of the communication bit-rate minimally required for solvability of various control and observation tasks is conceptually and computationally related to the classic concept of the topological entropy (TE) [10,18] and its recent control-oriented analogs [4][5][6][7]14,20,30,36,46,49]. Meanwhile, computation or even estimation of the TE of nonlinear systems has earned the reputation of an intricate matter; this intricacy briskly grows up with the system's dimension.…”