A contract negotiation scheme for safety verification of interconnected systems

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