Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts
For control engineers designing safety-critical network systems, this work provides a scalable method to verify set invariance, though it is incremental as it extends existing assume-guarantee and pSTL techniques.
This paper proposes an assume-guarantee reasoning approach to compute robust invariant sets for network systems, using parameterized signal temporal logic (pSTL) for subsystem contracts. The method achieves linear complexity for sparse networks and, combined with control barrier functions, ensures subsystem states remain within robust invariant sets.
This paper presents an assume-guarantee reasoning approach to the computation of robust invariant sets for network systems. Parameterized signal temporal logic (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 can be proved with a valid assume-guarantee contract by reasoning about individual subsystems. If a valid assume-guarantee contract with monotonic pSTL template is known, it can be further refined by value iteration. When such a contract is not known, an epigraph method is proposed to solve for a contract that is valid, ---an approach that has linear complexity for a sparse network. A microgrid example is used to demonstrate the proposed method. The simulation result shows that together with control barrier functions, the states of all the subsystems can be bounded inside the individual robust invariant sets.