Deep neural network based adaptive learning for switched systems

TL;DR

This paper introduces a deep neural network based adaptive learning method for switched systems, effectively handling structural changes by adaptively decomposing data and hierarchically constructing networks to identify switching times.

Contribution

The paper proposes a novel DNN-AL approach that adaptively decomposes data and hierarchically constructs networks to identify switching times in systems with structural changes.

Findings

Efficient training through parameter reuse at successive iterations.

Bounds of prediction error are established for the DNNs.

Numerical studies demonstrate the method's effectiveness.

Abstract

In this paper, we present a deep neural network based adaptive learning (DNN-AL) approach for switched systems. Currently, deep neural network based methods are actively developed for learning governing equations in unknown dynamic systems, but their efficiency can degenerate for switching systems, where structural changes exist at discrete time instants. In this new DNN-AL strategy, observed datasets are adaptively decomposed into subsets, such that no structural changes within each subset. During the adaptive procedures, DNNs are hierarchically constructed, and unknown switching time instants are gradually identified. Especially, network parameters at previous iteration steps are reused to initialize networks for the later iteration steps, which gives efficient training procedures for the DNNs. For the DNNs obtained through our DNN-AL, bounds of the prediction error are established. Numerical studies are conducted to demonstrate the efficiency of DNN-AL.