Coupled Controls-Computational Fluids Approach for the Estimation of the Concentration From a Moving Gaseous Source in a 2-D Domain With a Lyapunov-Guided Sensing Aerial Vehicle

The estimation of the gas concentration (process state) associated with an emitting stationary or moving source using a sensing aerial vehicle (SAV) is considered. The dispersion from such a gas source into the ambient atmosphere is representative of accidental or deliberate release of chemicals, or release of gases from the biological systems. Estimation of the concentration field provides a superior ability for source localization, assessment of possible adverse impacts, and eventual containment. The abstract and finite-dimensional approximation framework present couples theoretical estimation and control with computational fluid dynamics methods. The gas dispersion (process) model is based on the 2-D advection-diffusion equation with variable eddy diffusivities and ambient winds. The state estimator is a modified Luenberger observer with a collocated filter gain that is parameterized by the position of the SAV. The process-state (concentration) estimator is based on a 2-D adaptive, multigrid, multistep finite-volume method. The grid is adapted with local refinement and coarsening during the process-state estimation, to improve accuracy and efficiency. The 2-D motion dynamics of the SAV is incorporated into the spatial process and the SAV's guidance is directly linked to the performance of the state estimator. The computational model and the state estimator are coupled in the sense that grid refinement is affected by the SAV repositioning, and the guidance laws of the SAV are affected by grid refinement. Extensive numerical simulations serve to demonstrate the effectiveness of the coupled approach.