ResEntSG: Restoration entropy estimation for dynamical systems via Riemannian metric optimization

Abstract

In the remote state estimation problem, an observer reconstructs the state of a dynamical system at a remote location, where no direct sensor measurements are available. The estimator only has access to information sent through a digital channel. The notion of restoration entropy provides a way to determine the smallest channel capacity above which an observer can be designed that observes the system without a degradation of the initial estimation error. In general, restoration entropy is hard to compute. We present a class library in C++, that estimates the restoration entropy of a given system by computing an adapted metric for the system. The library is simple to use and implements a version of the subgradient algorithm for geodesically convex functions to compute an optimal metric in a class of conformal metrics. Included in the software are three example systems to demonstrate the use and efficacy of the library.

Keywords

• Restoration entropy
• Subgradient algorithm
• Geodesic convexity
• Riemannian metric
• Dynamical systems
• C++