Chemical Reactor Estimation Based on Sensors Network with Dropouts

In this paper, the estimation problem for the chemical reactor is considered. The model of measurement contains random variables with Bernoulli distribution, which are associated with dropouts. The anisotropy level for extended vector of input sequence is bounded by given positive value a. The input-to-estimation error system is described in terms of time-varying system with multiplicative noises. The boundedness of anisotropic norm for input-to-estimation error system is reduced to convex optimisation problem.

I. Introduction

The problem of disturbance rejection remains one of the biggest problem in the control theory. There are a lot of approaches have been studied, and some of them are based on stochastic properties of disturbances acting on the dynamic system. These approaches can be sensitive to disturbance uncertainties, hence robust methods of disturbance rejection should be developed. For this reason, anisotropy-based theory can be applied for estimation problem. Originally, a deterministic state space description for time-varying systems was considered in anisotropy-based theory [1]. Analysis for stochastic systems was investigated in [2]. The studied problem of analysis concerned the system with random matrices in the state space description. It allowed to consider anisotropy-based analysis for multiplicative noise systems. In spite of first approximation for solution was suggested in [3], the state space formula for anisotropic norm of multiplicative noise system was derived in [4]. For time-invariant systems with multiplicative noise, approximate calculation of anisotropic norm was considered in [5], and [6] contains the precise method of anisotropic norm calculation.