Synthesis of interconnected control systems under reachability specifications

In this work we synthesize constrained control laws in a compositional way to enforce a reachability specification for an interconnected control system. We first synthesize for each system a controller enforcing a local reachability specification using linear feasibility programs. Then within the framework of parametric assume-guarantee contracts, which encode the behavior of a control system in a parametric domain, we establish a small gain theorem guaranteeing the overall specification after interconnecting the systems together. The resulting controller could then be implemented in a decentralized, distributed, or mixed setup. We also show the effectiveness of our approach with a room temperature control example.