Parameter Synthesis for Hybrid Systems with an Application to Simulink Models

This paper addresses a parameter synthesis problem for nonlinear hybrid systems. Considering a set of uncertain parameters and a safety property, we give an algorithm that returns a partition of the set of parameters into subsets classified as safe, unsafe, or uncertain, depending on whether respectively all, none, or some of their behaviors satisfy the safety property. We make use of sensitivity analysis to compute approximations of reachable sets and an error control mechanism to determine the size of the partition elements in order to obtain the desired precision. We apply the technique to Simulink models by combining generated code with a numerical solver that can compute sensitivities to parameter variations. We present experimental results on a non-trivial Simulink model of a quadrotor helicopter.