The identification of switched systems is a challenging problem, which entails both combinatorial (sample-mode assignment) and continuous (parameter estimation) features. A general framework for this problem has been recently developed, which alternates between parameter estimation and sample-mode assignment, solving both tasks to global optimality under mild conditions. This article extends this framework to the nonlinear case, which further aggravates the combinatorial complexity of the identification problem, since a model structure selection task has to be addressed for each mode of the system. To solve this issue, we reformulate the learning problem in terms of the optimization of a probability distribution over the space of all possible model structures. Then, a randomized approach is employed to tune this distribution. The performance of the proposed approach on some benchmark examples is analyzed in detail.

交换系统的识别是一个具有挑战性的问题，它既需要组合（采样模式分配）又需要连续（参数估计）功能。最近已经开发出用于此问题的通用框架，该框架在参数估计和样本模式分配之间交替，从而在温和条件下将两个任务都求解为全局最优。本文将这个框架扩展到非线性情况，这进一步加剧了识别问题的组合复杂性，因为必须为系统的每种模式解决模型结构选择任务。为了解决这个问题，我们根据所有可能模型结构空间上的概率分布的优化来重新构造学习问题。然后，采用随机方法调整此分布。