Fault diagnosis in nonlinear differential-algebraic systems via an iterative learning observer

The problem of fault detection and estimation in a class of nonlinear differential-algebraic systems (NDAS), using an Iterative Learning Observer (ILO), is investigated in this paper. An NDAS is in a semi-explicit form with the differential variables coupled with the algebraic variables. In order to estimate the algebraic variables directly, an algorithm is developed to reconstruct the algebraic variables by converting a singular distribution matrix to a nonsingular one, using a series of elementary matrix operations followed by differentiation. An ILO is designed based on the reconstructed algebraic variables such that the estimated states, including both the differential and algebraic variables, converge to the actual values. The stability of the proposed observer is established and an illustrative example is provided to show the effectiveness of this new scheme. Keywords. Nonlinear Differential-Algebraic Systems, Algebraic Variable Conversion, Iterative Learning Observer, Faults, Fault Estimation.