Distributed Model Predictive Control for Linear Systems with Adaptive Terminal Sets
For control engineers designing distributed controllers for large-scale linear systems, this work addresses a known bottleneck of empty or small terminal sets in DMPC, but the improvement is incremental as it extends existing synthesis methods.
This paper proposes a distributed model predictive control (DMPC) scheme for linear constrained systems with separable structure, where the terminal controller and invariant terminal set are synthesized jointly within the DMPC formulation, unlike existing decoupled approaches. The method is validated on benchmark problems, showing improved feasibility and performance.
In this paper, we propose a distributed model predictive control (DMPC) scheme for linear time-invariant constrained systems which admit a separable structure. To exploit the merits of distributed computation algorithms, the stabilizing terminal controller, value function and invariant terminal set of the DMPC optimization problem need to respect the loosely coupled structure of the system. Although existing methods in the literature address this task, they typically decouple the synthesis of terminal controllers and value functions from the one of terminal sets. In addition, these approaches do not explicitly consider the effect of the current state of the system in the synthesis process. These limitations can lead the resulting DMPC scheme to poor performance since it may admit small or even empty terminal sets. Unlike other approaches, this paper presents a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the DMPC formulation. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the value function and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several examples including a benchmark spring-mass-damper problem.