Numerical approximation of the data-rate limit for state estimation under communication constraints

Abstract: In networked control, a fundamental problem is to determine the smallest capacity of a communication channel between a dynamical system and a controller above which a prescribed control objective can be achieved. Often, a preliminary task of the controller, before selecting the control input, is to estimate the state with a sufficient accuracy. For time-invariant systems, it has been shown that the smallest channel capacity $C_0$ above which the state can be estimated with an arbitrarily small error, depending on the precise formulation of the estimation objective, is given by the topological entropy or a quantity named restoration entropy, respectively. In this paper, we propose an algorithm that computes rigorous upper bounds of $C_0$, based on previous analytical estimates.