Model Predictive Real-Time Monitoring of Linear Systems

The predictive monitoring problem asks whether a deployed system is likely to fail over the next T seconds under some environmental conditions. This problem is of the utmost importance for cyber-physical systems, and has inspired real-time architectures capable of adapting to such failures upon forewarning. In this paper, we present a linear model-predictive scheme for the real-time monitoring of linear systems governed by time-triggered controllers and time-varying disturbances. The scheme uses a combination of offline (advance) and online computations to decide if a given plant model has entered a state from which no matter what control is applied, the disturbance has a strategy to drive the system to an unsafe region. Our approach is independent of the control strategy used: this allows us to deal with plants that are controlled using model-predictive control techniques or even opaque machine-learning based control algorithms that are hard to reason with using existing reachable set estimation algorithms. Our online computation reuses the symbolic reachable sets computed offline. The real-time monitor instantiates the reachable set with a concrete state estimate, and repeatedly performs emptiness checks with respect to a safety property. We classify the various alarms raised by our approach in terms of what they imply about the system as a whole. We implement our real-time monitoring approach over numerous linear system benchmarks and show that the computation can be performed rapidly in practice. Furthermore, we also examine the alarms reported by our approach and show how some of the alarms can be used to improve the controller.