Adaptive Control of 2-D PDEs Using Mobile Collocated Actuator/Sensor Pairs With Augmented Vehicle Dynamics

The main focus of this work is on the inclusion of vehicle dynamics for the control of spatially distributed processes utilizing mobile actuators and sensors. It is assumed that spatially collocated actuator/sensor pairs, affixed on vehicles, are capable of moving within the spatial domain and a combined control law-plus-guidance law is proposed in order to better address the effects of spatiotemporally varying disturbances. The proposed control architecture is simplified by using static output feedback combined with adaptation of the feedback gains. A Lyapunov redesign approach is employed to derive the guidance laws via the appropriate use of the vehicle control torques. Such guidance laws are gradient-based and tend to move the vehicle to spatial locations with large spatial gradients. The novelty here is that vehicle dynamics are directly coupled to the process dynamics and their motion is solely and explicitly dictated by the control performance of the spatially distributed process. Extensive numerical studies of a 2-D diffusion PDE with a mobile robot are included and which demonstrate the effectiveness of the proposed combined control law-plus-guidance law.