2020/05/05 by Kawan, C., Matveev, A., Pogromsky, A.
#37A35 #93B07 #94A17 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2005.02112
In the context of control and estimation under information constraints, restoration entropy measures the minimal required data rate above which the state of a system can be estimated so that the estimation quality does not degrade over time and, conversely, can be improved. The remote observer here is assumed to receive its data through a communication channel of finite bit-rate capacity. In this paper, we provide a new characterization of the restoration entropy which does not require to compute any temporal limit, i.e., an asymptotic quantity. Our new formula is based on the idea of finding a specific Riemannian metric on the state space which makes the metric-dependent upper estimate of the restoration entropy as tight as one wishes.