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：基于状态相关Riccati方程的非线性反馈设计方法已较为成熟，但由于计算代价过高而难以应用于大规模系统。若能将系统嵌入具有仿射线性参数依赖关系的线性变参数系统框架，则非线性反馈律可展开为常系数且可预计算的级数形式。本文提出一种通用方法对非线性系统进行近似，使得即使对于高维系统也能高效实现上述级数展开。我们以不可压缩Navier-Stokes方程的镇定问题作为应用场景，讨论了所涉及矩阵值方程的数值求解方法，并通过数值算例验证了该方法的有效性。