Multiple-Model Estimation with Variable Structure—Part II: Model-Set Adaptation

An important, natural, and practical approach to variable-structure multiple-model (VSMM) estimation is the recursive adaptive model-set (RAMS) approach. The key to this approach is model-set adaptation (MSA), which is both theoretically and practically challenging. This paper makes theoretical contributions to MSA. Various representative problems of MSA are formulated in terms of testing hypotheses that are in general composite, -ary, multivariate, and, worst of all, not necessarily disjoint. A number of sequential solutions are presented, which are computationally highly efficient, are easy to implement, and have some desirable optimality properties. These results form a theoretical foundation for developing good, general and practical MSA algorithms. Simulation results are provided to illustrate the usefulness and effectiveness of the solutions. The theoretical results presented herein have been applied to several RAMS algorithms in the subsequent parts of this series that are generally applicable, easily implementable, and significantly superior to the best fixed-structure MM estimators available. They are also important for model-set comparison, choice, and design for variable-structure as well as fixed-structure MM estimation.