Decentralized Signal Temporal Logic Control for Perturbed Interconnected Systems via Assume-Guarantee Contract Optimization

We develop a novel decentralized control method for a network of perturbed linear systems with dynamical couplings subject to Signal Temporal Logic (STL) specifications. We first transform the STL requirements into set containment problems and then we develop controllers to solve these problems. Our approach is based on treating the couplings between subsystems as disturbances, which are bounded sets that the subsystems negotiate in the form of parametric assume-guarantee contracts. The set containment requirements and parameterized contracts are added to the subsystems' constraints. We introduce a centralized optimization problem to derive the contracts, reachability tubes, and decentralized closed-loop control laws. We show that, when the STL formula is separable with respect to the subsystems, the centralized optimization problem can be solved in a distributed way, which scales to large systems. We present formal theoretical guarantees on robustness of STL satisfaction. The effectiveness of the proposed method is demonstrated via a power network case study.