State Estimation of a Spatial 2-D Linear Diffusion Process With Mobile Sensors

This paper studies the state observer design of a spatial two-dimensional (2-D) linear diffusion process described by a linear parabolic partial differential equation (PDE) under mobile sensors. Firstly, we analyze the well-posedness of the PDE system and give the structure form of the state observer with mobile sensors. Subsequently, according to the number of mobile sensors, the 2-D space domain is divided into multiple sub-domains, and the mobile sensors are guided by the projection operator method, which can guarantee that the mobile sensors can only move in their respective 2-D sub-domains. Then, in the light of Lyapunov theory, Poincaré-Wirtinger inequality and Barbalat lemma, we propose an observation-plus-guidance design method to ensure the asymptotic stability of the state estimation error system. In the designed mobile strategy, the actual guidance of mobile sensors is essentially a physical synthesis of two direction guidance laws, where two dimensional guidance laws are designed separately. Moreover, the existence condition of the observer is given by linear matrix inequalities. At last, a numerical example is provided to demonstrate the efficacy of the proposed design scheme.