Estimation and Control of 3D Diffusion-Advection System by Partial Differential Neural Network Combined With Divide-Space Sampling Strategy

In this paper, an optimization framework of partial differential neural network combined with divide-space sampling (PDNN-DSS) is proposed to solve the estimation and control problem of 3D diffusion-advection systems. The PDNN-DSS framework contains a divide-space sampling observer, a model prediction estimator, and a partial differential neural network solver. First, the open-loop state of the diffusion-advection system is obtained by designing the division space observer. The observer provides a deployment scheme for sensors so that mobile robots only need to carry actuators not sensors. Then, the control problem is transformed into an optimization problem by designing a model prediction estimator. Subsequently, a novel partial differential neural network is designed. The neural network is based on partial differential equations containing spatial diffusion features and can solve spatio-temporal optimization problems. Finally, the effectiveness of the proposed method in this paper is demonstrated through simulations from multi-dimensional perspectives of 2D and 3D diffusion-advection systems.