Abstract
AbstractThe 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.
Funder
gruppo nazionale per l’analisi matematica, la probabilità e le loro applicazioni
engineering and physical sciences research council
cnpq
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Reference53 articles.
1. Albi, G., Bicego, S., Kalise, D.: Gradient-augmented supervised learning of optimal feedback laws using state-dependent Riccati equations. IEEE Control Syst. Lett. 6, 836–841 (2022)
2. Alla, A., Falcone, M., Saluzzi, L.: An efficient DP algorithm on a tree-structure for finite horizon optimal control problems. SIAM J. Sci. Comput. 41(4), A2384–A2406 (2019)
3. Antoulas, A.C.: Approximation of Large-scale Dynamical Systems. Advances in Design and Control. SIAM, Philadelphia (2005)
4. Azmi, B., Kalise, D., Kunisch, K.: Optimal feedback law recovery by gradient-augmented sparse polynomial regression. J. Machin. Learn. Res. 22(48), 1–32 (2021)
5. Banks, H.T., Lewis, B.M., Tran, H.T.: Nonlinear feedback controllers and compensators: A state-dependent riccati equation approach. Comput. Optim. Appl. 37(2), 177–218 (2007)
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