An enhanced L₂ state estimation for linear parabolic PDE systems with mobile sensors

This paper studies an enhanced L₂ 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 L₂ 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 L₂ performance bound as small as possible, a suboptimal enhanced L₂ 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.