摘要：AbstractThe two-tank problem is often considered as a challenging benchmark problem of process control, owing to its non-linear nature and non-minimum phase behavior. Non-linearity arises due to the dependence of non-linear outlet flow associated with the tank level. Hence, it is significant to investigate the dynamics of the system. This paper utilizes a novel idea of transforming the non-linear Stochastic Differential Equations (SDEs) to an appropriate form of the SDEs that preserves non-linear effects. In this paper, first, the Carleman linearization technique is explored to arrive at the bi-linearized two-tank SDEs. Then, we utilize the Fokker-Planck equation for the estimation of the bi-linearized two-tank problem. The theoretical results corroborated with numerical simulations highlight the effectiveness of the proposed Carleman linearization-based estimation method in contrast to the benchmark EKF-prediction method, i.e. without observation.
关键词：KeywordsState estimationCarleman linearizationKronecker productItôStochastic differential ruleFokker-Planck equationtwo-tank system
