Summary: Convergence Rate of Quantization Error in Networked Control Systems
Hui Fang and Panos J. Antsakls
In this paper, we investigate the problem of convergence
rate of the quantization error in networked control systems.
Given bit rate R, we derive the best convergence rate of the
quantization error together with a corresponding rate al-
location strategy. Specifically, using a min-max eigenvalue
problem (MMEP) formulation, it is shown that the error
convergence rate is determined by the ratio between |detA|
and R where A is the state matrix. It is also shown that the
bit rate R can be optimized through a dynamic quantization
policy among the unstable modes of the system, such that
the convergence rate of the quantization error approaches
the optimal solution to the MMEP problem.
There is strong ongoing interest in the problem of con-
trol under communication constraints; attempting to bring
together classical control theory and practical communi-
cation theoretical issues in the design of control system.