Low-complexity robust decentralized MPC: a foundational algorithm for constrained coalitional control

We present a low-complexity robust decentralized MPC formulation for linear time-invariant subsystems that are subject to state and input constraints and coupled via dynamics. The proposed approach is a simple application of tube-based robust MPC to each subsystem, but with some enhancements that make the scheme more applicable to problems with higher-order subsystem dynamics, such as those arising in coalitional control: we remove explicit reliance on invariant sets, and achieve robust stability and feasibility via simple constraint scalings, determined by solving an LP. In the second part of the paper, we apply the approach to coalitional constrained control, and develop theoretical results on recursive feasibility under time-varying coalitions, including the existence of finite dwell times for coalitional switching.