Modular Computation of Restoration Entropy for Networks of Systems: A Dissipativity Approach

The problem of state estimation based on information received over a finite bit rate channel gives rise to the study of minimal bit rate above which state can be estimated with any desired accuracy. In the past few years, researchers have studied the minimal average bit rate which is sufficient enough for state estimation such that the estimation error stays within a given factor of its initial value. The notion of restoration entropy characterizes this type of bit rate. Recent results proposed numerical schemes to estimate restoration entropy by the computation of singular values of the linearized systems. Such schemes are either complex to implement or suffer severely from computational complexity and the size of the state dimension. In this letter, we describe a
modular
approach to compute an upper bound of the restoration entropy of a large network by decomposing the network to an interconnection of smaller subsystems. Then, we formulate a distributed optimization problem which is solved for each subsystem separately and then their optimization results are composed to get an upper bound of the restoration entropy for the overall network. We illustrate the effectiveness of our results by two examples.