Nonlinear feedback design via state-dependent Riccati equations is well established but unfeasible for large-scale systems because of computational costs. If the system can be embedded in the class of linear parameter-varying (LPV) systems with the parameter dependency being affine-linear, then the nonlinear feedback law has a series expansion with constant and precomputable coefficients. In this work, we propose a general method to approximating nonlinear systems such that the series expansion is possible and efficient even for high-dimensional systems. We lay out the stabilization of incompressible Navier-Stokes equations as application, discuss the numerical solution of the involved matrix-valued equations, and confirm the performance of the approach in a numerical example.

翻译：通过状态依赖Riccati方程的非线性反馈设计已有深入研究，但由于计算成本过高，难以应用于大型系统。如果系统能够嵌入具有仿射线性参数依赖关系的线性参数变化（LPV）系统类别中，则非线性反馈定律具有常数和可预先计算系数的级数展开式。在本工作中，我们提出了一种通用的方法来近似非线性系统，使得级数展开式即使在高维系统中也是可能且有效的。我们提出了通过数值解求解所涉及的矩阵值方程的不可压纳维-斯托克斯方程的稳定化应用，并在一个数值示例中验证了该方法的性能。