Modelos Locais Crescentes e Robustos a Outliers para Identificação Recursiva de Sistemas Dinâmicos

Abstract

The tasks of identification and modeling of dynamical systems are fundamental in modern control. For example, models are used to obtain adequate approximations of the response of the system to be controlled. Roughly, these models can be classified into two groups: global models or local models. Global models use only a single mathematical structure to represent the entire domain of the problem. Local models, in their turn, partition the problem domain into smaller regions so that a simpler model can be adopted for each region. A major disadvantage of local models is the need to specify the number of submodels before training. A possible solution involves the use of growing models. Regardless of the model’s structure, it is desirable that the structure be capable of handling outlying samples, providing robustness to the model robustness in real-world applications. That said, this thesis aims to review the design of local models based on vector quantization in order to extend the applicability of such models, whether of fixed or increasing size, for robust recursive identification of nonlinear dynamic systems. The models chosen for this purpose use variants of the LMS (least mean square) rule , chosen due to its low computational cost for parameter estimation, and an outlier-robust rule, based on the framework of M estimation, which is obtained directly from the LMS rule without additional cost. The chosen models were the following: the local linear mapping (LLM), the radial basis functions network (RBFN), the local model network (LMN). From these models, incremental and robust variants for recursive identification of dynamic systems were developed, namely, RAN-LMS, G-LMN and ORG-LMN. The proposed models have the following characteristics: increasing online structure, fast recursive update rules, better memory usage (it is not necessary to estimate the inverse of the covariance matrix as required in the RLS rule) and robustness to outliers. In this sense, efficiency in performance and simplicity of implementation are the essential qualities of the proposed approaches. The models were tested in a free simulation scenario and were

evaluated by two metrics: (i) mean squared error and (ii) Kolmogorov-Smirnov test. A com- prehensive assessment involving two sets of synthetic data and five sets of real data, including a large-scale data set and a MIMO data set, corroborates the superior predictive performance of the proposed approaches in scenarios contaminated by outliers compared to alternative models.