Recent Results in State Estimation of Dynamical Systems with Inputs under Bandwidth Constraints

Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. We present two notions of topological entropy, one to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ε. The other is to do the same but to estimate the state of a switched system with unknown switching signal up to an error that is bounded by ε for τ seconds after each switch and then decays exponentially at a rate of α till the next switch. Since computation of entropy is hard in general, we present upper bounds on both notions of entropy. Finally, we present preliminary results on the relation between the two notions. Note that most of the ideas presented in this abstract are from our papers [4] and [5].