An enhanced state estimation for linear parabolic PDE systems with mobile sensors

Abstract

This paper studies an enhanced  2 state estimation problem of distributed parameter processes modeled by a linear parabolic partial differential equation using mobile sensors. The proposed estimation scheme contains a state estimator and the guidance of mobile sensors, where the spatial domain is decomposed into multiple subdomains according to the number of sensors and each sensor is capable of moving within the respective subdomain. The state estimator is desired to make the state estimation error system exponentially stable while providing an  2 performance bound. The mobile sensor guidance is used to enhance the transient performance of the error system. By the Lyapunov direct technique, an integrated design of state estimator and mobile sensor guidance laws is developed in the form of bilinear matrix inequalities (BMIs) to meet the desired design objectives. Moreover, to make the  2 performance bound as small as possible, a suboptimal enhanced  2 state estimation problem is formulated as a BMI optimization one, which can be solved via an iterative linear matrix inequality algorithm. Finally, numerical simulations are given to show the effectiveness of the proposed method.KEYWORDS distributed parameter processes, exponential stability, mobile sensor guidance, parabolic partial differential equation, state estimation 1552

State estimation for linear time‐delay distributed parameter systems with mobile sensors

“…As in References 21 and 23, in order to avoid the mobile sensors colliding with each other and achieving the observer design objective, we always hope that the $$$ i $$$th sensor only can move in the space domain $$$ {\Omega}_{i\varepsilon} $$$, (i.e., $$$ {x}_i^a(t)\in {\Omega}_{i\varepsilon} $$$, ), where $$$ \kappa >1 $$$ is a design parameter. To meet this expectation, we will introduce a projection operator and give an important lemma.…”

“…However, the main objective of References 19 and 20 is just for the sake of designing the guidance laws of mobile sensors, such that the system estimation performance is improved. Different from References 19 and 20, in Reference 21, not only the state observer with a guaranteed $$$ {\mathcal{L}}_2 $$$ performance but also the mobile sensor guidance were simultaneously designed for linear parabolic DPSs, where the state observer rendered the estimation error system exponentially stable while providing an $$$ {\mathcal{L}}_2 $$$ performance bound, and the mobile sensor guidance enabled the estimation error converges to zero more quickly. Under mobile sensing measurements, the less conservative switching state observer design was developed for semilinear parabolic DPSs 22 .…”