Wei Xing Zheng

Qian Feng, Wei Xing Zheng, Xiaoyu Wang et al.

This paper introduces an effective framework for designing memoryless dissipative full-state feedback for general linear delay systems via the KrasovskiÄ­ functional (KF) approach, where an arbitrary finite number of pointwise and general distributed delays (DDs) exists in the state, input and output. To handle the infinite dimensionality of DDs, we employ the Kronecker-Seuret Decomposition (KSD) which we recently proposed for analyzing matrix-valued functions in the context of delay systems. The KSD enables factorization or least-squares approximation of any number of $\fL^2$ DD kernels from any number of DDs without introducing conservatism. This also facilitates the construction of a complete-type KF with flexible integral kernels by means of a novel integral inequality derived from the least-squares principle. Our solution includes two theorems and an iterative algorithm to compute controller gains without relying on nonlinear solvers. A numerical example is tested to show the effectiveness of the proposed approach.

Hongpeng Zhou, Chahine Ibrahim, Wei Xing Zheng et al.

This paper proposes a sparse Bayesian treatment of deep neural networks (DNNs) for system identification. Although DNNs show impressive approximation ability in various fields, several challenges still exist for system identification problems. First, DNNs are known to be too complex that they can easily overfit the training data. Second, the selection of the input regressors for system identification is nontrivial. Third, uncertainty quantification of the model parameters and predictions are necessary. The proposed Bayesian approach offers a principled way to alleviate the above challenges by marginal likelihood/model evidence approximation and structured group sparsity-inducing priors construction. The identification algorithm is derived as an iterative regularised optimisation procedure that can be solved as efficiently as training typical DNNs. Remarkably, an efficient and recursive Hessian calculation method for each layer of DNNs is developed, turning the intractable training/optimisation process into a tractable one. Furthermore, a practical calculation approach based on the Monte-Carlo integration method is derived to quantify the uncertainty of the parameters and predictions. The effectiveness of the proposed Bayesian approach is demonstrated on several linear and nonlinear system identification benchmarks by achieving good and competitive simulation accuracy. The code to reproduce the experimental results is open-sourced and available online.