Prognosis based on the Joint Parameter/State Estimation Using Zonotopic LPV Set-Membership Approach

Abstract

Abstract This paper addresses the problem of prognostics based on Joint Estimation of States and Parameters (JESP) using a zonotopic Linear Parameter-Varying (LPV) set-membership approach. The aim of the prognostics is to forecast the Remaining Useful Life (RUL) of systems with degraded components. Thus, this paper suggests transforming such systems with nonlinear dynamical models into an LPV representation. Hence, a Zonotopic Set-Membership (ZSM) observer has been proposed to carry out the JESP for degradation assessment with a considerable focus on multiple-output systems. Despite the existence of different geometrical shapes, zonotopes have gained recently a lot of popularity due to their low computational complexity, in addition to the possibility of relating them with stochastic approaches. Moreover, an optimal correcting gain has been designed based on Linear Matrix Inequality (LMI) for robust observer tuning. Additionally, the LMI-based tuning can be solved offline with reduced computational effort while coping with a polytopic LPV representation of the model. Consequently, a Recursive ZSM (RZSM) approach has been employed for degradation prediction and guaranteed zonotopic RUL forecasting. Finally, the proposed approach is assessed using a degraded power electronics system, and the results are illustrated.