Guaranteed State Estimation and Fault Detection based on Zonotopes for Differential-Algebraic-Equation Systems

This paper presents a set-membership approach based on zonotopes for differential-algebraic-equation (DAE) systems with unknown-but-bounded disturbances and noise, which can be subsequently used for guaranteed state estimation and fault detection. Complex systems are usually modeled by differential and algebraic equations, where differential equations describe system dynamics and additionally, algebraic equations represent the static relations. The proposed algorithm provides a way to propagate a zonotopic set that contains the system states not only consistent with the measurement outputs but also constrained with their static relations. Finally, a real application has been presented to verify the proposed approach.