(243a) Optimal Subsystem Decomposition of Process Networks for Distributed State Estimation Based on Weighted Graph

A medium- to large-scale process usually comprises components that interconnect with each other through mass and energy flows tightly. Advanced control systems are essential for such processes to meet strict regulations and to achieve desired level of safety, sustainability and profitability. Unfortunately, commonly used centralized control designs are not capable of handling these processes considering their relatively large scales and the complex and integrated structures. During the past decade, we have witnessed a rapid trend moving away from the centralized control architecture towards distributed control architectures for improved computational efficiency, maintenance flexibility and fault tolerance capability [1-3]. A successful distributed control system design involves two key steps: 1) to decompose the entire process into smaller subsystems properly; and 2) to propose a cost-effective control algorithm based on which local controllers can be developed and the communication protocol can be determined. In this work, we focus on the topic of subsystem decomposition.

In literature, subsystem decomposition and configuration has been mainly considered in the context of distributed control (see, e.g., [4-7]). The equally important topic – subsystem decomposition for distributed state estimation has not been extensively investigated. In [8], an initial attempt was made to decompose a nonlinear system into smaller units considering the structural closeness between different state and output measurement variables. In [9], distributed state estimation and control were jointly considered in one framework. A community detection based approach was proposed to recommend subsystem models that are appropriate for both local estimator and controller designs [10-11]. The two methods only take into account the physical topology of a process, yet overlook the strength of the connectivity among different variables. As a result, they may not suffice to give good decompositions for complex process networks where strength levels of the interconnections are vastly different.

Motivated by the above observations, we aim to propose a systematic subsystem decomposition approach for distributed state estimation by considering the strength in coupling as well. We borrow the idea of community structure detection that has been successfully used in subsystem configuration for distributed control (see, e.g., [4], [6], [7]) to determine optimal subsystems structures for distributed state estimation. Specifically, a directed network is formed for a nonlinear process. In the constructed network, state and measured output variables are treated as nodes, which are connected via weighted edges. The weighted directed graph is used to characterize both the connectivity and sensitivities of the edges that connect between state and output variables. Community structure detection is used to divide all the variables into smaller groups, such that the intra-connection within each group is made much stronger than the interaction among different groups. Subsystem models that are appropriate for distributed state estimation are configured based on the variables assigned to the groups. Both numerical and process examples are used for illustration. Subsystem models are formed, and distributed state estimation schemes are developed based on the recommended models. The results confirm better estimation performance using the subsystem structure recommended by the proposed method, and the necessity of incorporating edge weights in subsystem decomposition for distributed state estimation.

References

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