State observers with random sampling times and convergence analysis of double-indexed and randomly weighted sums of mixing processes. (English) Zbl 1219.93139

Le Van Thanh; Yin, G. George; Wang, Le Yi

SIAM J. Control Optim. 49, No. 1, 106-124 (2011).

Summary: Algorithms for system identification, estimation, and adaptive control in stochastic systems rely mostly on different types of signal averaging to achieve uncertainty reduction, convergence, stability, and performance enhancement. The core of such algorithms is various types of laws of large numbers that reduce the effect of noises when they are averaged. Many of the noise sequences encountered are often correlated and non-white. In the case of state estimation using quantized information such as in networked systems, convergence must be analyzed on double-indexed and randomly weighted sums of mixing-type stochastic processes, which are correlated with the remote past and distant future being asymptotically independent. This paper presents new results on convergence analysis of such processes. Strong laws of large numbers and convergence rates for such problems are established. These results resolve some fundamental issues in state observer designs with random sampling times, quantized information processing, and other applications.

MSC:

93E12	Identification in stochastic control theory
60F15	Strong limit theorems
93E24	Least squares and related methods for stochastic control systems
93E35	Stochastic learning and adaptive control
93B30	System identification
93C57	Sampled-data control/observation systems

Keywords:

randomly weighted sum; mixing sequence; double-indexed sum; triangular array; state observer; quantized information