(295a) Partition-Based Distributed Extended Kalman Filter for Large-Scale Nonlinear Processes with Application to Wastewater Treatment System

A typical process network comprises multiple operating units/subsystems interconnected through material, energy, and information flows. Due to the interaction of these subsystems and the nonlinearity of the dynamic process, developing and implementing control systems for process networks can be challenging [1][2]. To ensure operational safety, profitability, and environmental sustainability, advanced control solutions are needed. The partition-based distributed control architecture has emerged as a promising framework for large-scale and complex processes. Distributed state estimation is an essential component for establishing a complete distributed control system. Distributed moving horizon estimation (DMHE) has been considered a powerful solution to distributed state estimation problems, since it can simultaneously handle scalability, nonlinearity, and constraints on state variables and disturbances [3][4]. Meanwhile, when priority should be given to improving computational efficiency or when constraints do not need to be imposed, it is worthwhile to consider recursive methods such as distributed extended Kalman filter as an alternative solution, such that optimization can be avoided and good estimates can be obtained in a more efficient manner. In this work, we plan to propose a partition-based DEKF method with local estimators being developed based on partitioned subsystem models, to estimate the full-state of general nonlinear processes in real-time.

To achieve this objective, first, we propose a partition-based distributed Kalman filter (DKF) algorithm that can provide guaranteed performance for linear systems. Then, the DKF algorithm is extended to DKEF through successive local linearization of the subsystem models. Typically, the DKF algorithms can be divided into two categories: (a) consensus-based Kalman filter; (b) partition-based Kalman filter. Within the consensus-based framework, local estimators are developed based on a global model, and each local estimator estimates the aggregate states of the entire system. A consensus protocol is then employed to collect local state estimates to facilitate an agreement on the estimates among the local estimators [5][6]. In terms of the partition-based Kalman filter, the entire system is divided into smaller subsystem models, and the local estimators are designed based on the corresponding subsystem models. In a partition-based distributed design, each estimator provides the estimates of the state of the corresponding subsystem only, which is a subset of the state variables of the entire process [7][8][9]. While there have been some results on partition-based DKF, some assumptions have been made on the subsystem model, which have limited the wide adoption of these approaches in large-scale process applications. For example, in [7], it is assumed there is no coupling between subsystems. In [8], the author assume the interaction between subsystems is only caused by the measurable states. In [9], it is assumed that the estimation error system of its proposed DKF algorithm should be able to be described by a directed acyclic graph.

Based on the above observations, we focus on the development of a new partition-based solution for general large-scale nonlinear systems that consist of multiple interconnected subsystems. First, we develop a non-iterative distributed full-information state estimation formulation, of which the objective function for each subsystem is created through partitioning the objective function of centralized full-information estimation and including sensitivities of the local objective function to sensor measurements of the interacting subsystems. Second, we leverage the formulated distributed full-information estimation to derive and obtain a DKF algorithm. The stability of the proposed DKF algorithm is rigorously proved. Finally, we extend this stability-guaranteed DKF to address nonlinear estimation problems of large scales. The formulated partition based DEKF approach is applied to a large-scale wastewater treatment process for estimating 145 state variables based on limited sensor measurements.

References

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