A guided search framework in multiple model control

Wei Gao, Liting Sun, Masayoshi Tomizuka

Abstract: The idea of using multiple models to cope with parameter uncertainties in adaptive systems was first introduced in the 1990s. Conventionally, methods based on this mechanism typically suffer from “curse of dimension,” which means that the number of required identification models grows exponentially with respect to the number of unknown parameters. In this paper, the parameter identification problem is formulated as a time-varying optimization procedure, and a guided multiple model search framework is proposed to solve it. Instead of sampling the identification models in a large parameter space, models are sampled locally and used to estimate the search direction. As a result, the number of needed identification models grows linearly in this approach, in comparison with the exponential growth of existing methods. The proposed method also provides a unified form for nonlinear systems with non-affine unknown parameters, which is out of the scope of classical adaptive control theory. Moreover, theoretical convergence analysis is provided with specific conditions. The effectiveness of the proposed approach is verified by simulations and comparisons with existing methods.