Observer canonical form based robust fault detection and estimation for hyperbolic spatiotemporal dynamic systems

In this study, the authors propose a novel state and a fault estimation scheme for a class of hyperbolic spatiotemporal dynamic systems in the presence of unknown external disturbance. They consider the occurrence of multiplicative actuator and sensor faults. In detail, they consider two cases of fault occurrence: (i) only one type (actuator or sensor) of fault happens; (ii) two types of faults occur simultaneously. This study discusses the fault detectability conditions by proposing a fault detection observer. To complete the estimation problem, three difficulties arise: (i) no prior information shows the type of faults; (ii) the observer design is non‐linear due to multiplication between plant signals (state or input) and unknown fault parameters; (iii) only one boundary measurement is available. They convert the original faulty plant into its observer canonical form. By proposing two filters based on the resulting observer canonical form, they develop novel parameter update laws for fault parameter estimation. With the proposed update laws, the true state of the faulty plant can be estimated by the proposed observers. By selecting appropriate Lyapunov functions, they prove that estimation error of state and fault parameters exponentially decays to an arbitrarily small neighbourhood of zero despite unknown external disturbance.