Identification and Response Prediction of Switching Dynamic Systems Using Interval Analysis

Abstract

A novel method based on interval analysis is proposed in this work for modeling and response prediction of SISO uncertain switching dynamic systems. To describe the system’s dynamic in any operating mode, a local linear model is used. The validity domain of any local model is determined in system’s input-output space. To take into account the modeling error, adjustable parameters of local models are considered time-varying and characterized by intervals of real numbers. A model whose parameters are characterized by intervals is called an interval model. A procedure is also developed to perform nstep prediction of system’s response using the multi-mode interval model. Since the model parameters are intervals, the predicted response at any instant is not a real number anymore but an interval of real numbers. The set of predicted intervals at different instances generates a tube through time called wrapping envelope. However, the identification/characterization procedure proposed in the early stage of this work guarantees that the wrapping envelope includes the system’s response taking into account possible modeling error and perturbations. This envelope can be used in diagnosis to supervise healthy operation of the system as well as in process safety analysis to guarantee that the physical variables of the system never enter in forbidden operating zones and the system remains in safe operating conditions.