Coordinating distributed MPC efficiently on a plantwide scale: The Lyapunov envelope algorithm

The model predictive control (MPC) of large-scale systems should adopt a distributed optimization approach, where controllers for the constituent subsystems optimize their control actions and iterations are used to coordinate their decisions. The real-time implementation of MPC, however, usually allows very limited time for computation and inevitably needs to be terminated early. In this work, we propose a splitting algorithm for distributed optimization analogous to forward-backward splitting (FBS), where ℓ₁ and quadratic penalties are imposed on the violation of interconnecting relations among the subsystems. By designing the involved parameters based on dissipative analysis, the iterations result in the monotonic decrease of a plant-wide Lyapunov function, which we call Lyapunov envelope, thus maintaining closed-loop stability under distributed MPC despite early termination and yielding improving control performance as the allowed computational time or number of iterations increases. The proposed Lyapunov envelope algorithm is tested on an industrial-scale vinyl acetate monomer process.