Guidance of Mobile Actuator-Plus-Sensor Networks for Improved Control and Estimation of Distributed Parameter Systems

This paper presents an abstract framework for the optimization of actuating and sensing devices in distributed parameter systems. The optimization is performed on the repositioning of these devices throughout the spatial domain. It is assumed that a network of mobile sensing and actuating devices is available to obtain measurements from the spatially distributed process and dispense control signals to the spatially distributed process. By taking advantage of the properties that the spatial operator that governs the process dynamics possesses, namely symmetry, coercivity and boundedness, a scheme for the guidance of a mobile actuator-plus-sensor network is developed and used for the performance enhancement of the spatial process. The class of systems is governed by diffusion PDEs equipped with actuators having a boxcar spatial distribution and a collocated sensing device that provides the spatially averaged state measurement over the range of the actuating device. Using Lyapunov stability arguments, a stable guidance scheme is provided for each of the mobile agents. Due to the specific structure of the closed loop system operator with time-varying input and output operators, the same guidance schemes are applicable to the dual problem of mobile sensors employed for enhancing the state estimation problem. Both a centralized state estimator with mobile sensors and a network of consensus distributed estimators are considered, since both filters can be shown to result in the specific algebraic structure of a symmetric spatial operator with collocated input and output operators. Extensive numerical simulations for a 1-D diffusion equation with two actuator/sensor agents, a 2-D diffusion equation with one collocated actuator/sensor agent plus a centralized filter for a 1-D diffusion equation are included to verify the effectiveness of a such a mobile actuator-plus-sensor network in suppressing the effects of spatially varying disturbances and enhancing the system's performance.