Abstract : The paper proposes a new homogeneous observer for finite-dimensional projections of quadratic homogeneous hyperbolic PDEs with compact state space. The design relies upon new sufficient conditions for fixed-time convergence of observer's gain, described as a solution of a non-linear homogeneous matrix differential equations, towards an ellipsoid in the space of symmetric non-negative matrices. Convergence of the observer is analyzed, and a numerical convergence test is proposed: numerical experiments confirm the test on ODEs obtained by finite-difference discretization of Burgers-Hopf equation.
https://hal.inria.fr/hal-02904474
Contributor : Andrey Polyakov <>
Submitted on : Wednesday, July 22, 2020 - 11:20:19 AM Last modification on : Friday, December 11, 2020 - 6:44:08 PM Long-term archiving on: : Tuesday, December 1, 2020 - 4:16:09 AM
Sergiy Zhuk, Andrey Polyakov. Homogeneous Observers for Projected Quadratic Partial Differential Equations. IEEE Conference on Decision and Control, Dec 2020, Jesu Island, South Korea. ⟨hal-02904474⟩