Deep neural network based adaptive learning for switched systems

. In this paper, we present a deep neural network based adaptive work based methods are actively developed for learning governing equations in unknown dynamic systems. However, 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 change 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 provides efficient training procedures for the DNNs. For the DNNs obtained through our DNN-AL, the bounds of the prediction error are established. Numerical studies are conducted to demonstrate the efficiency of DNN-AL.