Deep neural network based adaptive learning for switched systems
This work addresses a domain-specific problem for researchers in control systems or dynamic modeling, offering an incremental improvement over existing methods for switched systems.
The paper tackles the problem of learning governing equations in switched systems, where structural changes degrade deep neural network efficiency, by proposing a DNN-AL approach that adaptively decomposes data and reuses parameters, resulting in established prediction error bounds and demonstrated efficiency in numerical studies.
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.