(664f) Dynamic Graph-Based Distributed Estimation and Control of Fast-Evolving Complex Process Networks

Model Predictive Control (MPC) is widely utilized in chemical process manufacturing and energy systems for executing optimal decision-making and control actions, owing to its adaptability, inherent robustness, and capability to effectively manage complex multivariable systems subject to operational and safety constraints [1]. MPC formulates the control problem as a dynamic optimization problem that must be solved frequently at every sampling interval to determine the optimal set of manipulated inputs [2,3]. Therefore, the feasibility of using MPC hinges on its ability to solve the underlying dynamic optimization problem in real-time, subject to the process model and constraints. This restricts the MPC implementation in a centralized manner, particularly for large-scale integrated processes. Distributed Model Predictive Control (DMPC) presents a viable alternative to the centralized MPC approach, potentially speeding up optimization through parallel computing while preserving a desired degree of control performance. DMPC decomposes the optimal control problem into smaller subproblems solved by cooperative control agents.

Decomposing a system is the initial step in implementing a distributed control architecture, identifying the optimal number of subsystems and the distribution of inputs and outputs among them. Effective decompositions are those that reduce the required communication between control agents, thereby lowering computational demands. From the network theory perspective, this problem can be represented by identifying subsystems with minimal interconnections but strongly related variables [4]. Methods like input-output connectivity clustering have been suggested to create a system decomposition hierarchy [5]. Moreover, community detection approaches have been applied to the graph representation of the systems to identify highly interconnected subsystems by maximizing a modularity index, which measures the extent of edge concentration within communities compared to a hypothetical random graph [7-9]. Case studies were conducted on various process networks, including a benchmark reactor-separator, benzene alkylation with ethylene, and an amine gas treatment facility, exploring diverse optimization frameworks, communication strategies among local controllers, and model uncertainty considerations. These studies have demonstrated that community detection-based decompositions of unweighted graph representations can accelerate computations without substantially compromising performance compared to the centralized approach [10-13]. Our recent work has shown superior distributed estimation and control performance utilizing weighted graph-based system decomposition over unweighted [14,15], while the weighted graphs only captured variable interactions at a steady state.

This work focuses on developing an adaptive distributed estimation and control architecture using dynamic graph-based community detection, where the distributed structure is recursively modified at each sampling time. Modularity is employed as the primary metric for community detection. However, the NP-hardness of maximizing modularity makes resolving at each sampling time impractical. Our alternative approach involves pre-clustering and updating the subsystems as needed during the transition. The proposed decomposition approach limits the number of variables allowed to participate in the community update at each sampling time. The proposed dynamic graph-based system community detection approach is then employed to develop an integrated distributed moving horizon estimation (DMHE) and DMPC design to address the output tracking problem. The adaptive distributed estimation and control approach is implemented for a benzene alkylation process benchmark. The closed-loop performance illustrates that employing dynamic weighted graph models for community detection of the integrated process representation enhances distributed state estimation and output tracking, surpassing the traditional approaches based on unweighted and steady state-weighted decompositions.

References:

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[14] Ebrahimi, A.; Pourkargar, D. B. Distributed Model Predictive Control of Integrated Process Networks Based on an Adaptive Community Detection Approach. In Proceedings of the American Control Conference, 2024, in press.

[15] Ebrahimi, A.; Pourkargar, D. B. Distributed Estimation and Control of Process Networks using Adaptive Community Detection. In Proceedings of the IFAC Symposium on Advanced Control of Chemical Processes, 2024, in press.