The optimization problem in model predictive control (MPC) algorithm for piecewise affine (PWA) systems often contains substantial logic variables, which requires extensive computing power for online implementation. This paper proposes a one-step distributed MPC algorithm for spatially interconnected PWA systems with both input and state constraints, where the algorithm is based on a series of $r$-step robustly controllable sets. Algorithms for offline computing terminal sets and a series of $r$-step robustly controllable sets are developed using the step-by-step backward approach. The states that lie in the robustly controllable sets are steered into the terminal set in finite steps and ultimately converge into a robustly positively invariant set. The proposed algorithm is demonstrated to significantly reduce the online computational burden. Simulation results are provided to showcase the effectiveness of the algorithm.

分段仿射 (PWA) 系统的模型预测控制 (MPC) 算法中的优化问题通常包含大量逻辑变量，需要大量的计算能力才能在线实现。本文提出了一种用于具有输入和状态约束的空间互连 PWA 系统的单步分布式 MPC 算法，该算法基于一系列$r$-step 鲁棒可控集。离线计算终端机算法等一系列$r$-step 稳健可控集是使用逐步向后的方法开发的。位于鲁棒可控集合中的状态以有限步骤被引导到终端集，并最终收敛到鲁棒正不变集。所提出的算法被证明可以显着降低在线计算负担。仿真结果展示了算法的有效性。