Runtime Monitoring of Stochastic Cyber-Physical Systems with Hybrid State

Correct functioning of cyber-physical systems is of critical importance. This is more so in the case of safety critical systems such as in medical, automotive and many other applications. Since verification of correctness, in general, is infeasible and testing is not exhaustive, it is of critical importance to monitor such system during their operation and detect erroneous behaviors to be acted on. A distinguishing property of cyber-physical systems is that they are described by a mixture integer-valued and real-valued variables. As a result, approaches that assume countable number of states are not applicable for runtime monitoring of such systems. This paper proposes a formalism, called Extended Hidden Markov systems, for specifying behavior of systems with such hybrid state. Using measure theory, it exactly characterizes when such systems are monitorable with respect to a given property. It also presents monitoring algorithms and experimental results showing their effectiveness.