# State-dependent Riccati equation feedback stabilization for nonlinear PDEs

arXiv: https://arxiv.org/abs/2106.07163 · HTML: https://mlsanity.com/paper/2106.07163/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2021.

## Built on by (most cited first, 3 of 3)

- [PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods](https://mlsanity.com/paper/2604.04920/) (2026)
- [Data/moment-driven approaches for fast predictive control of collective dynamics](https://mlsanity.com/paper/2402.15611/) (2024)
- [Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design](https://mlsanity.com/paper/2403.18044/) (2024)

## Abstract (arXiv)

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.