Adaptive Control of Flow and Mass Transport by Multi-Sensor Arrays

 

Professor Nikolaos Katopedes
 
University of Michigan
Department of Civil and Environmental Engineering

 

A method is presenting that can be potentially used to arrest and eliminate a toxic plume or a water wave.  The fundamental hypothesis is that there exist boundary mechanisms that, if activated at the right place and time, they can effectively eliminate the threat with minimum delay.  Furthermore, the method relies on multiple sensor arrays to detect and rapidly transmit current information about the plume or wave to the model.  Adaptive control  is then achieved by history matching of appropriate boundary controls.  The execution can be made in real time by solving the corresponding adjoint equations.  Sensitivity expressions relating the objective function response to perturbations in boundary controls are derived for nonlinear flow equations using an adjoint sensitivity formalism that does not require the assumption of compact support of the adjoint variables or strong dissipation of the flow variables.  The approximate Riemann invariants of the adjoint problem are shown to transmit sensitivity information in the reverse time direction along the characteristic paths of the basic problem.  The use of these approximate Riemann invariants gives rise to non-reflective inflow and outflow boundary conditions for the adjoint problem that permit sensitivities to be accurately determined.  Examples are presented for the mitigation of catastrophic waves and toxic plumes.

 

Friday, March 28, 2003

3:30 – 4:30 p.m.

1500 EECS