Set Membership Adaptive Non Parametric Identification of Non-Linear Systems

Abstract

Adaptation is a desirable feature when dealing with the identification of complex systems. However, this property can be difficult to achieve when non-convex model structures such as neural networks are employed to parametrize the unknown system. This work introduces a novel approach for dynamically adapting the data set that defines the model in non-parametric Set Membership identification methods. The proposed solution constructs a nonparametric, nonlinear model of a discrete-time dynamical system by exploring the data set, assuming the system follows a Nonlinear Auto-Regressive model with exogenous Inputs (NARX) structure. The identification data are assumed to be affected by unknown but bounded noise. Specifically, two strategies are proposed to adapt the identification data set while preserving system performance dynamically. The first strategy allows the data set to incorporate new data as novel modeling information becomes available, while redundant information can be eliminated when memory conditions are reached. The second strategy introduces new information sequentially; once an auxiliary memory vector in the data set reaches its desired cardinality, the method orderly replaces the oldest data with newer dynamics. These strategies enable the identified models to adapt in response to unmodeled behaviors arising from time-varying dynamics or limited initial data sets, minimizing the need for extensive experimentations and allowing to dynamically reconstruct the data set for developing data-driven models. The effectiveness of the proposed approaches is demonstrated through the experimental modeling of a nonlinear mechatronic system. Performance is benchmarked against neural network models and a static Set Membership identification strategy. Results indicate that the proposed dynamic data set generation approach improves the accuracy and robustness of the model when using non-informative experimental data sets as starting point for the estimation, improving the overall performance of the data-driven modeling task and facilitating the use of these modeling techniques in real environments.