论文标题
非线性系统识别，具有吸引力区域的先验知识
Nonlinear System Identification with Prior Knowledge of the Region of Attraction
论文作者
论文摘要
当在平衡点的吸引力区域（ROA）上可用时，我们会考虑非线性系统识别的问题。我们以优化问题的形式提出了一种识别方法，将拟合误差最小化并保证所需的稳定性属性。通过联合识别验证稳定性属性的动力学和Lyapunov功能来解决问题。在这种情况下，假设集是一个繁殖的内核希尔伯特空间，就ROA给定子集的每个点而言，Lyapunov函数的谎言衍生物不平等施加了约束。问题是无限量优化的非凸线，并具有无限数量的约束。为了获得可拖动的公式，仅考虑一个适当设计的有限子集。由此产生的问题以线性组合及其衍生物的线性组合形式接受解决方案。在线性和双线性约束下，具有二次成本函数的等效优化问题。合适的变量更改可以对问题进行凸的重新重新重新制定。为了减少超参数的数量，优化问题适用于对角核的情况。该方法是通过示例来证明的。
We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing the fitting error and guaranteeing the desired stability property. The problem is approached by joint identification the dynamics and a Lyapunov function verifying the stability property. In this setting, the hypothesis set is a reproducing kernel Hilbert space, and with respect to each point of the given subset of the ROA, the Lie derivative inequality of the Lyapunov function imposes a constraint. The problem is a non-convex infinite-dimensional optimization with infinite number of constraints. To obtain a tractable formulation, only a suitably designed finite subset of the constraints are considered. The resulting problem admits a solution in form of a linear combination of the sections of the kernel and its derivatives. An equivalent optimization problem with a quadratic cost function subject to linear and bilinear constraints is derived. A suitable change of variable gives a convex reformulation of the problem. To reduce the number of hyperparameters, the optimization problem is adapted to the case of diagonal kernels. The method is demonstrate by means of an example.
