This work proposes a state estimation strategy over mobile sensor–actuator networks with missing measurements for a class of distributed parameter systems (DPSs) with time-varying delay. Initially, taking advantage of the abstract development equation theory and operator semigroup method, this kind of delayed DPSs described by partial differential equations (PDEs) is derived for evolution equations. Subsequently, the distributed state estimators including consistency component and gain component are designed; the purpose is to estimate the original state distribution of the delayed DPSs with missing measurements. Then, a delay-dependent guidance approach is presented in the form of mobile control forces by constructing an appropriate Lyapunov function candidate. Furthermore, by applying Lyapunov stability theorem, operator semigroup theory, and a stochastic analysis approach, the estimation error systems have been proved asymptotically stable in the mean square sense, which indicates the estimators can approximate the original system states effectively when this kind of DPS has time-delay and the mobile sensors occur missing measurements. Finally, the correctness of control strategy is illustrated by numerical simulation results.
Stabilization of time-delay systems with a Controlled time-varying delay and applications