Data‐driven identification and control of nonlinear systems using multiple NARMA‐L2 models

Abstract

Summary The multiple model approach provides a powerful tool for identification and control of nonlinear systems. Among different multiple model structures, the piecewise affine (PWA) models have drawn most of the attention in the past two decades. However, there are two major issues for the PWA model‐based identification and control: the curse of dimensionality and the computational complexity. To resolve these two issues, we propose a novel multiple model approach in this paper. Different from PWA models in which all dimensions of the regressor space are engaged in the partitioning, the key idea of the proposed multiple model architecture is to partition only the range of the control input u(k) at time k (the instant of interest in the control problem) into several intervals and identify a local model that is linear in u(k) within each interval. On the basis of Taylor's theorem, a theoretical upper bound for the approximation error of the model structure can also be obtained. With the proposed multiple model architecture, a switching control algorithm is derived to control nonlinear systems on the basis of the weighted one‐step‐ahead predictive control method and constrained optimization techniques. In addition, the upper bound for the tracking error using this switching control strategy is also analyzed rigorously under certain assumptions. Finally, both simulation studies and experimental results demonstrate the effectiveness of the proposed multiple model architecture and switching control algorithm. Copyright © 2017 John Wiley & Sons, Ltd.

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“…Recently, its efficiency was also examined for the ILI purpose in References 48 and 49. The multiple model approach was shown to provide a powerful tool for identification of nonlinear systems, in Reference 50. The key idea is to partition only the range of the control input into several intervals and identify a local model that is linear in the control input in each interval.…”

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