Safety analysis using compositional bounded error approximations of communicating hybrid systems

In this paper, we consider the problem of bounded safety verification of networked hybrid systems that communicate during discrete transitions using synchronization actions and input variables that receive information about the state of the communicating automata. We propose a compositional framework based on bounded error approximations which reduces the bounded safety verification to the satisfiability checking problem for a formula that is constructed in a compositional manner, by first constructing formulae that encode the approximate executions of the component hybrid systems, then composing these in a sound manner to obtain a formula encoding the executions of the networked hybrid system, and finally restricting it to encode those executions that reach a given unsafe region. We illustrate the compositional analysis framework on a case study involving an aircraft collision avoidance protocol by using a piecewise bilinear approximation of the system dynamics.