Distributed model predictive control for reconfigurable systems based on Lyapunov analysis. (March 2023) - Zheng, Yi; Li, Shaoyuan; Wan, Ruoxiao; Wu, Zhe; Zhang, Yueyan
Abstract: This paper focuses on Distributed Model Predictive Control (DMPC) for systems composed of many interacting subsystems, in the case that process topology changes, e.g., the isolation of a part of subsystems due to system maintenance, or processing change due to production change. The reconfiguration of the process may cause the Model Predictive Control (MPC) optimization problem infeasible for the updated system. The proposed DMPC is based on Lyapunov techniques. After discussing the reasons causing infeasibility of the reconfigured system (violation of constraints), a transition optimization problem of each subsystem-based MPC is designed for the case that the topology change cannot be conducted immediately, which focuses on steering the states that will remain in the updated system into the region that makes the updated system feasible. Besides, to enlarge the attraction region of each subsystem-based MPC, an auxiliary variable is added to the optimization problem as a decision variable. The auxiliary variable is a steady state and the MPC lets the state track this auxiliary variable. The distance between the auxiliary variable and the set-point is also minimized in each subsystem-based optimization problem. The Lyapunov constraints which consider the auxiliary variable are designed to guarantee that the state converges to a small region around the set-point. The stability analysis and an application to a chemical process example are presented to show the effectiveness of the proposed method. Highlights: A DMPC is designed for processes composed of interacting subsystems, in the case that parts of the process topology change. The reasons causing in-feasibility of the reconfigured system are discussed. An LDMPC with an enlarged attraction region that integrates terminal equilibrium calculation into its optimization problem. The designed Lyapunov constraints considering the time-varying equilibrium, which guarantees the stability of the closed-loop reconfigurable system. A transition optimization problem of each subsystem-based MPC is designed for expediting the topology change of the process.