Synthesis of separable controlled invariant sets for modular local control design

Many correct-by-construction control synthesis methods suffer from the curse of dimensionality. Motivated by this challenge, we seek to reduce a correct-by-construction control synthesis problem to subproblems of more modest dimension. As a step towards this goal, in this paper we consider the problem of synthesizing decoupled robustly controlled invariant sets for dynamically coupled linear subsystems with state and input constraints. Our approach, which gives sufficient conditions for decoupled invariance, is based on optimization over linear matrix inequalities which are obtained using slack variable identities. We illustrate the applicability of our method on several examples, including one where we solve local control synthesis problems in a compositional manner.