A robust fault detection filter for polynomial nonlinear systems via sum-of-squares decompositions

A novel diagnostic framework is discussed for fault detection of nonlinear systems whose structure is described by multivariate polynomials. The trade-off between disturbance rejection and fault sensitivity prescriptions is characterized via algebraic geometry conditions and the unknown input observer design problem is formulated via sum-of-squares (SOS) technicalities by exploiting the results of the Positivstellensatz Theorem. An adaptive threshold logic is proposed to reduce the generation of false alarms, and the diagnostic filter capabilities are illustrated via a numerical example taken from the literature.