Luís A. Aguirre

Faizal Hafiz, Akshya Swain, Eduardo M. A. M. Mendes et al.

The present study proposes a simple grey-box identification approach to model a real DC-DC buck converter operating in continuous conduction mode. The problem associated with the information void in the observed dynamical data, which is often obtained over a relatively narrow input range, is alleviated by exploiting the known static behavior of buck converter as a priori knowledge. A simple method is developed based on the concept of term clusters to determine the static response of the candidate models. The error in the static behavior is then directly embedded into the multi-objective framework for structure selection. In essence, the proposed approach casts grey-box identification problem into a multi-objective framework to balance bias-variance dilemma of model building while explicitly integrating a priori knowledge into the structure selection process. The results of the investigation, considering the case of practical buck converter, demonstrate that it is possible to identify parsimonious models which can capture both the dynamic and static behavior of the system over a wide input range.

Antônio H. Ribeiro, Koen Tiels, Luis A. Aguirre et al.

The exploding and vanishing gradient problem has been the major conceptual principle behind most architecture and training improvements in recurrent neural networks (RNNs) during the last decade. In this paper, we argue that this principle, while powerful, might need some refinement to explain recent developments. We refine the concept of exploding gradients by reformulating the problem in terms of the cost function smoothness, which gives insight into higher-order derivatives and the existence of regions with many close local minima. We also clarify the distinction between vanishing gradients and the need for the RNN to learn attractors to fully use its expressive power. Through the lens of these refinements, we shed new light on recent developments in the RNN field, namely stable RNN and unitary (or orthogonal) RNNs.

Antônio H. Ribeiro, Luis A. Aguirre

We propose a new algorithm for estimating NARMAX models with $L_1$ regularization for models represented as a linear combination of basis functions. Due to the $L_1$-norm penalty the Lasso estimation tends to produce some coefficients that are exactly zero and hence gives interpretable models. The novelty of the contribution is the inclusion of error regressors in the Lasso estimation (which yields a nonlinear regression problem). The proposed algorithm uses cyclical coordinate descent to compute the parameters of the NARMAX models for the entire regularization path. It deals with the error terms by updating the regressor matrix along with the parameter vector. In comparative timings we find that the modification does not reduce the computational efficiency of the original algorithm and can provide the most important regressors in very few inexpensive iterations. The method is illustrated for linear and polynomial models by means of two examples.