Abstract
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.
Highlights
Mobile sensor and actuator networks have played a central role in the artificial intelligence (AI) engineering based on wireless communication technology, which are upgraded of traditional fixed sensor–actuator networks
We suppose that one sensor and one actuator in the mobile sensor–actuator networks are collocated into a same device, which is denoted as θia (t) = θis (t) = θi (t), the spatial distribution functions b(z; θia (t)) and c(z; θis (t)) are given by b(z; θi (t)) = c(z; θi (t))
The two questions raised above will be solved by using the Lyapunov stability method and stochastic analysis approach; the main results are given by the following theorem
Summary
Mobile sensor and actuator networks have played a central role in the artificial intelligence (AI) engineering based on wireless communication technology, which are upgraded of traditional fixed sensor–actuator networks. By utilizing the Lyapunov technique, operator semigroup method and mobile sensor/actuator networks to make stability analysis achieved better control performance. The team of Demetriou has not considered the estimation problem with missing measurements; this issue of state estimation with missing measurements has been addressed in [44,47] based on the achievements of Demetriou, whereas they have not taken the time delay phenomenon into account in the distributed parameter systems. Drawing inspiration of the above research achievements, we consider the state estimation problem for a class of distributed parameter systems with time-varying delay over mobile sensor–actuator networks with missing measurements. The control forces of mobile sensor–actuator have been designed by utilizing mobile sensor–actuator networks and Lyapunov functional technology, which have enhanced the estimators performance and made the state of estimation error systems converge to zero faster than that of fixed sensor–actuator networks.
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