Lebesgue approximation model of continuous-time nonlinear dynamic systems

Traditional model-based approaches are based on periodic iterations, where the continuous-time model is discretized with a fixed period. Despite the easiness in analysis and design, such periodic approximation model may be undesirable from the computation-efficiency point of view. This paper presents the Lebesgue-approximation model (LAM) of continuous-time nonlinear systems, where the iteration is activated on an “as-needed” basis, but not periodically. We show that the proposed LAM behaves exactly the same as a specific event-triggered feedback system, through which the properties of the LAM can be studied. We provide a sufficient condition to ensure asymptotic stability of the LAM and derive theoretical bounds on the difference between the states of the LAM and the original continuous-time system. The LAM is then integrated in the particle-filtering approach for fault prognosis. Simulation results show that the LAM can dramatically reduce the number of iterations in prognosis without sacrificing accuracy and precision.