Observers and Optimal Estimation for PDE Systems

Wednesday, September 6, 2017 - 1:15pm - 1:50pm
Lind 305
John Burns (Virginia Polytechnic Institute and State University)
The application of PDE Kalman filtering for optimal sensor location goes back more than 45 years. A theoretical treatment of the optimal sensor location problem was first rigorously developed by Alain Bensoussan in his 1972 paper (although Falb's 1967 paper hinted at this idea. In the 1970s this was a purely theoretical result and not computationally feasible. Today this approach to sensor location is possible on most desktop workstations and has resulted in new applications to very challenging problems. The current challenge is to apply this idea to mobile sensor systems where the sensor location is moving along a path in $3$D space. Once again, computational complexity is the bottleneck and new ideas are needed to address this issue. In this presentation we discuss a history of these ideas, point to new challenges and offer some potential solutions to the computational bottlenecks. In particular, we discuss Chandrasekhar factorization and multi-domain computational schemes which have already produced real time solutions. Finally, we close with some comments on how higher order DG methods and GPU computing might be used to achieve real time optimal sensor systems.