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 2 and ∞ 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.

Alla A., Kalise D., Simoncini V. (2023). State-dependent Riccati equation feedback stabilization for nonlinear PDEs. ADVANCES IN COMPUTATIONAL MATHEMATICS, 49(1), 1-32 [10.1007/s10444-022-09998-4].

State-dependent Riccati equation feedback stabilization for nonlinear PDEs

Simoncini V.
Ultimo
Writing – Original Draft Preparation
2023

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 2 and ∞ 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.
2023
Alla A., Kalise D., Simoncini V. (2023). State-dependent Riccati equation feedback stabilization for nonlinear PDEs. ADVANCES IN COMPUTATIONAL MATHEMATICS, 49(1), 1-32 [10.1007/s10444-022-09998-4].
Alla A.; Kalise D.; Simoncini V.
File in questo prodotto:
File Dimensione Formato  
s10444-022-09998-4.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 2.46 MB
Formato Adobe PDF
2.46 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/950624
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact