Compositional Synthesis of Decentralized Robust Set-Invariance Controllers for Large-scale Linear Systems

Abstract: Ensuring constraint satisfaction in large-scale systems with hard constraints is vital in many safety critical systems. The challenge is to design controllers that are efficiently synthesized offline, easily implementable online, and provide formal correctness guarantees. In this paper, we provide a method to compute correct-by-construction controllers for a network of coupled linear systems with additive bounded disturbances such that i) the design of the controllers is fully compositional - we use an optimization-based approach that iteratively computes subsystem-level assume-guarantee contracts in the form of robust control invariant sets; and ii) the controllers are decentralized hence online implementation requires only the local state information. We present illustrative examples, including a case study on a system with 1000 dimensions.