State-dependent Riccati equation feedback stabilization for nonlinear PDEs
Abstract
The synthesis of suboptimal feedback laws for controlling nonlinear dynamics arising from semi-discretized PDEs is studied. An approach based on the State-dependent Riccati Equation (SDRE) is presented for H2 and Hinf control problems. Depending on the nonlinearity and the dimension of the resulting problem, offline, online, and hybrid offline-online alternatives to the SDRE synthesis are proposed. The hybrid offline-online SDRE method reduces to the sequential solution of Lyapunov equations, effectively enabling the computation of suboptimal feedback controls for two-dimensional PDEs. Numerical tests for the Sine-Gordon, degenerate Zeldovich, and viscous Burgers' PDEs are presented, providing a thorough experimental assessment of the proposed methodology.
Keywords
Cite
@article{arxiv.2106.07163,
title = {State-dependent Riccati equation feedback stabilization for nonlinear PDEs},
author = {Alessandro Alla and Dante Kalise and Valeria Simoncini},
journal= {arXiv preprint arXiv:2106.07163},
year = {2021}
}