Optimal level-crossing prediction for jump linear MIMO dynamical systems

In this article, the theoretically optimal prediction of level-crossings for a jump linear MIMO (multi-input/multi-output) dynamical system driven by a control input is investigated. The study of this problem is motivated by the practical implications for design of an optimal alarm system as applied to the advance prediction of adverse events, which will elicit the fewest false alarms for a fixed detection probability. It was found that using an additional control input term results in increased uncertainty due to the associated model for the control. However, using the appropriate condition for optimality provides an accommodation for this uncertainty which does not translate into compromised predictive capability. For the given application, it was observed that modeling the control input as a linear dynamical system results in better prediction performance and qualitatively has a higher model fidelity than when using a hidden Markov model for the same function.