(40c) Subsystem Decomposition of Process Networks for Simultaneous Distributed State Estimation and Control
Subsystem decomposition may affect the performance of a distributed predictive control system significantly. The community detection concept originating from network theory provides a very promising way to address the subsystem decomposition problem [4, 6]. By means of the measure of modularity , community-based approaches have been proposed to find distributed control structures where the subsystems are made well-decoupled [8, 4]. It is worth mentioning that the existing methods require a full state feedback. However, full state measurements can be difficult to obtain online for many applications. One solution is to incorporate distributed state estimation and distributed control in one integration, such that distributed control can be implemented based on output measurements. From the perspective of implementation, maintenance and communication, it is more favorable if the local state estimators and local controllers are designed based on the same subsystem decomposition. However, a systematic approach to achieve this objective is not yet available.
In this work, we focus on subsystem decomposition of nonlinear process networks for simultaneous distributed state estimation and distributed control. To achieve this goal, we propose a systematic approach based on the concept of community structure detection. We resort to the measure of modularity to quantitatively assess the quality of different community structures. Specifically, the state, manipulated input and measured output variables of a process are taken into account and are viewed as vertices in a network. The way to construct a directed graph containing all the vertices and the corresponding adjacency matrix is defined. An implementation procedure based on approximate optimization of modularity is developed, such that subsystem models for simultaneous distributed state estimation and distributed control can be established by allocating vertices into communities based on modularity. Three chemical process examples of different complexities are used to illustrate the effectiveness and applicability of the proposed approach. While there have been several heuristic approaches on subsystem decomposition for distributed control (e.g., [8, 4]), to the best of our knowledge, the approach proposed in this work is the first one that enables a distributed scheme to require much less information from the process; that is, only output-feedback information is needed for distributed control design and implementation. Also, it is not a trivial extension of the existing approaches. Technical contributions of this work include the following aspects:
- an adjacency matrix which incorporates state, manipulated input, and measured output variables is defined;
- bidirectional edges are considered to characterize the connectivity between state and measured output variables and are used for constructing the direct graph and the adjacency matrix;
- a simple yet efficient method is proposed to calculate the adjacency matrix;
- a method for initializing the community structure is proposed to better handle the constraints on the subsystem structure;
- a systematic procedure is proposed based on the fast folding algorithm  to decompose the entire process network into subsystems of which the number is user-specified.
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