Switching state observer design for semilinear parabolic PDE systems with mobile sensors

Abstract

This paper studies the problem of state observation for a class of semilinear parabolic partial differential equation (PDE) systems using mobile sensors, where the spatial domain is decomposed into multiple subdomains according to the number of sensors and each sensor is able to move within the respective spatial subdomain. Initially, the well-posedness of the original parabolic PDE system is discussed. Subsequently, a mode indicator function is used to indicate the different modes for all sensors and a mode-dependent observation scheme is presented to reduce the conservatism of observer design. Then, by employing Lyapunov direct technique and Wirtinger’s inequality, an integrated design of switching state observers and mobile sensor guidance laws is developed in terms of linear matrix inequalities, such that the resulting state estimation error system is exponentially stable. Moreover, the mobile sensor guidance can enhance the transient performance of the error system. Finally, numerical simulations are given to illustrate the effectiveness of the proposed design method.