Synthesis of separable controlled invariant sets for modular local control design
For control engineers, this provides a sufficient condition to reduce computational complexity in modular control design, though the approach is incremental and limited to linear subsystems.
This paper addresses the curse of dimensionality in correct-by-construction control synthesis by decomposing the problem into lower-dimensional subproblems. The authors propose a method to synthesize decoupled robustly controlled invariant sets for dynamically coupled linear subsystems using linear matrix inequalities, demonstrating compositional local control synthesis on examples.
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.