Robust Zonotopic Prognostics Approaches for LPV Systems Based on Set-Membership and Extended Kalman Filter

Abstract

This paper proposes robust model-based prognostics approaches based on zonotopic Joint Estimation of States and Parameters (JESP) for Linear Parameter-Varying (LPV) systems. Zonotopes are employed due to their simple computations with a reduced number of vertices. Thus, Zonotopic Set-Membership (ZSM) and Zonotopic Extended Kalman Filter (ZEKF) approaches are investigated for the JESP which plays a crucial role in the proposed Prognostics and Health Management (PHM) approach. The zonotopic estimators are optimally-tuned using a specially formulated Linear Matrix Inequality (LMI) framework to guarantee a high estimation accuracy and less conservative results. Furthermore, a Recursive ZSM (RZSM) approach is derived from a conventional Recursive Least Squares (RLS) filter for the sake of Remaining Useful Life (RUL) forecasting of exponentially-decayed parameters. Additionally, a polynomial RUL forecasting approach has been also proposed based on the ZEKF approach. Finally, a degraded DC-DC converter is modelled as an LPV system and examined with the proposed approaches, and the obtained results show their efficiency.