Fault coverage modeling in nonlinear dynamical systems

In this paper, we propose an approach for modeling fault coverage in nonlinear dynamical systems. Fault coverage gives a measure of the likelihood that a system will be able to recover after a fault occurrence. In our setup, the system dynamics are described by a standard state-space model. The system input (disturbance) is considered to be unknown but bounded at all times. Before any fault occurrence, the vector field governing the system dynamics is such that, for any possible input signal, the corresponding system reach set is contained in some region of the state space defined by the system performance requirements. When a fault occurs, the vector field that governs the system dynamics might be altered. Fault coverage is defined as the probability that, given a fault has occurred, the system trajectories remain, at all times, within the region of the state-space defined by the performance requirements. Input-to-state stability (ISS) concepts are used to compute estimates of the proposed coverage model. Several examples are discussed in order to illustrate the proposed modeling approach.