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.

State-dependent Riccati equation feedback stabilization for nonlinear PDEs / Alla A.; Kalise D.; Simoncini V.. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - STAMPA. - 49:1(2023), pp. 9.1-9.32. [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
State-dependent Riccati equation feedback stabilization for nonlinear PDEs / Alla A.; Kalise D.; Simoncini V.. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - STAMPA. - 49:1(2023), pp. 9.1-9.32. [10.1007/s10444-022-09998-4]
Alla A.; Kalise D.; Simoncini V.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/950624
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