State-dependent Riccati equation feedback stabilization for nonlinear PDEs
State-dependent Riccati equation feedback stabilization for nonlinear PDEs
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DOI：
10.1007/s10444-022-09998-4
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发表时间：
2021-06
影响因子：
1.7
通讯作者：
A. Alla;D. Kalise;V. Simoncini
中科院分区：
文献类型：
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作者：
A. Alla;D. Kalise;V. Simoncini
研究了半离散偏微分方程非线性动力学控制的次优反馈律的综合问题。提出了一种基于状态相关Riccati方程（SDRE）的2和∞控制方法。根据所产生的问题，离线，在线和混合离线在线替代SDRE合成的非线性和尺寸。混合离线-在线SDRE方法减少到顺序的解决方案的李雅普诺夫方程，有效地使计算次优反馈控制的二维偏微分方程。正弦戈登，退化Zeldovich，和粘性Burgers的偏微分方程的数值试验，提供了一个彻底的实验评估所提出的方法。
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.