PhD Comprehensive Exam | Avneet Kaur, Neural networks-based state estimation

MS Teams (please email amgrad@uwaterloo.ca for the meeting link)

Candidate

Avneet Kaur | Applied Mathematics, University of Waterloo

Title

Neural networks-based state estimation

Abstract

State estimation of a dynamical system refers to estimating the state of a system given a model, measurements, and some information about the initial state. While Kalman filtering [1] does optimal state estimation of linear systems, optimal estimation of high order non-linear systems of ordinary differential equations is still an open problem. The research focuses on providing an optimal method for state estimation of such high order systems by using advancements in the field of data. We propose to use deep learning to estimate the state of a system and test our codes on discretization of systems of high-order ordinary differential equations derived from partial differential equations such as Kuramoto-Sivashinsky equation [2],wave equation [3] [4]and cantilevered Euler Bernoulli beam [5], [6]

References

[1]         D. Simon, Optimal State Estimation: Kalman, H∞, and Nonlinear approaches, Wiley-Interscience, 2006.

[2]         R. A. Jamal and K. A. Morris, "Linearized stability of partial differential equations with application to stabilization of Kuramoto-Sivashinsky equation," Siam Journal Control Optim., vol. 56, no. 1, pp. 120-147, 2015.

[3]         T. Khan, K. A. Morris and M. Stastna, "Computation of the optimal sensor location for the estimation of a 1D linear dispersive wave equation," American Control Conference, pp. 5270-5275, 2015.

[4]         T. Khan, "Optimal sensor location for the estimation of a linear dispersive wave equation," University of Waterloo, 2015.

[5]         K. A. Morris, Controller design for distributed parameter systems, Springer, 2020.

[6]         C. Navasca and K. A. Morris, "Approximation of low rank solutions for linear quadratic control of partial differential equations," Springer Comp. Optim. Appli., vol. 46, pp. 93-111, 2010.