变结构多模型(VSMM)估计的一个重要、自然和实用的方法是递归自适应模型集(RAMS)方法。此方法的关键是在理论上和实践上都具有挑战性的模型集自适应(MSA)。本文在理论上对MSA进行了研究。根据假设检验,阐明了MSA的各种典型问题,而这些假设一般是复合的,N元的,多变量的,更糟糕的是,不一定不相交。给出了一定数量的序列方案,这些方案在计算上都是高效的,容易实现的,并具有一些令人满意的最优特性。这些结果构成了建立性能良好,通用和实用的MSA算法的理论基础。在这里给出的理论结果已经应用于这系列后续部分的几种RAMS算法,这些算法都是应用广泛,容易实现并且明显优于当前的最佳固定结构多模型估计器。同时,它们对于变结构和固定结构多模型估计器的模型集对比、选择和设计都很重要。 An important, natural and practical method of Variable Structure Multi-Model (VSMM) estimation is the Recursive Adaptive Model Set (RAMS) method. The key to this approach is the theoretically and practically challenging Model Set Adaptation (MSA). In this paper, MSA has been studied theoretically. Based on hypothesis testing, various typical problems of MSA are clarified, and these assumptions are generally complex, N-ary, multivariate, and worse, and do not necessarily disjoint. A number of sequence schemes are given, which are computationally efficient, easy to implement, and have some of the most desirable features. These results form the rationale for establishing a well-performing, universal and practical MSA algorithm. The theoretical results presented here have been applied to several RAMS algorithms in subsequent parts of this series, all of which are widely used, easy to implement and significantly better than the current best fixed structure multi-model estimators. At the same time, they are very important for the model set comparison, selection and design of multi-model estimators with variable structure and fixed structure.