Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts

TL;DR

This paper introduces an assume-guarantee reasoning framework using parameterized STL to compute robust invariant sets in network systems, enabling scalable verification and control synthesis with a microgrid example.

Contribution

It develops a novel approach combining assume-guarantee contracts with pSTL for set invariance, including an epigraph method for contract synthesis in sparse networks.

Findings

The method successfully bounds subsystem states within invariant sets.

The approach scales linearly with network size in sparse systems.

Simulation confirms effectiveness with microgrid example.

Abstract

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.