Nonlinear Set Membership Regression with Adaptive Hyper-Parameter Estimation for Online Learning and Control.

Methods known as Lipschitz Interpolation or Nonlinear Set Membership regression have become established tools for nonparametric system-identification and data-based control. They utilise presupposed Lipschitz properties to compute inferences over unobserved function values. Unfortunately, it relies on the a priori knowledge of a Lipschitz constant of the underlying target function which serves as a hyperparameter. We propose a closed-form estimator of the Lipschitz constant that is robust to bounded observational noise in the data. The merger of Lipschitz Interpolation with the new hyperparameter estimator gives a new nonparametric machine learning method for which we derive sample complexity bounds and online learning convergence guarantees. Furthermore, we apply our learning method to model-reference adaptive control. We provide convergence guarantees on the closed-loop dynamics and compare the performance of our approach to recently proposed alternative learning-based controllers in a simulated flight manoeuvre control scenario

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Separated antecedent and consequent learning for Takagi-Sugeno fuzzy systems

In this paper a new algorithm for the learning of Takagi-Sugeno fuzzy systems is introduced. In the algorithm different learning techniques are applied for the antecedent and the consequent parameters of the fuzzy system. We propose a hybrid method for the antecedent parameters learning based on the combination of the Bacterial Evolutionary Algorithm (BEA) and the Levenberg-Marquardt (LM) method. For the linear parameters in fuzzy systems appearing in the rule consequents the Least Squares (LS) and the Recursive Least Squares (RLS) techniques are applied, which will lead to a global optimal solution of linear parameter vectors in the least squares sense. Therefore a better performance can be guaranteed than with a complete learning by BEA and LM. The paper is concluded by evaluation results based on high-dimensional test data. These evaluation results compare the new method with some conventional fuzzy training methods with respect to approximation accuracy and model complexity