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This paper presents an assume-guarantee reasoning approach to the computationof robust invariant sets for network systems. Parameterized signal temporallogic (pSTL) is used to formally describe the behaviors of the subsystems,which we use as the template for the contract. We show that set invariance canbe proved with a valid assume-guarantee contract by reasoning about individualsubsystems. If a valid assume-guarantee contract with monotonic pSTL templateis known, it can be further refined by value iteration. When such a contract isnot known, an epigraph method is proposed to solve for a contract that isvalid, ---an approach that has linear complexity for a sparse network. Amicrogrid example is used to demonstrate the proposed method. The simulationresult shows that together with control barrier functions, the states of allthe subsystems can be bounded inside the individual robust invariant sets.

Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts