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This paper proposes a (control) barrier function synthesis and safetyverification scheme for interconnected nonlinear systems based onassume-guarantee contracts (AGC) and sum-of-squares (SOS) techniques. It iswell-known that the SOS approach does not scale well for barrier functionsynthesis for high-dimensional systems. In this paper, we show thatcompositional methods like AGC can mitigate this problem. We formulate thesynthesis problem into a set of small-size problems, which constructs localcontracts for subsystems, and propose a negotiation scheme among the subsystemsat the contract level. The proposed scheme is then implemented numerically ontwo examples: vehicle platooning and room temperature regulation.

A contract negotiation scheme for safety verification of interconnected systems