Nonlinear multi-rate current state estimation: convergence analysis and application to biological systems

Abstract

In most nonlinear control systems, such as biochemical systems, only partial state variables can be reliably measured. Thus, there is a need to estimate the unavailable state variables. Further, to effectively monitor and operate the nonlinear process, a frequent estimation of those unavailable state variables is desired. However, in many cases, the measurable state variables usually can only be measured less frequently. Hence, multi-rate state estimation has received many attentions because it allows for using infrequently available measurements and it leads to considerable improvement in the estimation results. Many works implement the multi-rate estimator using the extended Kalman filters or nonlinear observers with numerical integration. However, numerical integration is a time-consuming process, and the convergence analysis of multi-rate state estimation was not addressed. This paper designs a multi-rate nonlinear estimator based on Taylor series expansion plus discrete-time nonlinear state transformation, and we analyze the condition for the asymptotical stability of the state estimation error. This paper applies the general results on the multi-rate state estimation to a class of biological systems. The comparative study between multi-rate and single-rate state estimation demonstrates the effectiveness of the proposed scheme. Although this work is motivated by the multi-rate state estimation of biological systems, the proposed scheme and the performed analysis have a larger applicability to many nonlinear systems.