Tai Weipeng, Li Xinling, Zhou Jianping, Arik Sabri
Research Institute of Information Technology, Anhui University of Technology, Ma'anshan, 243000, Anhui, China; School of Computer Science & Technology, Anhui University of Technology, Ma'anshan, 243032, Anhui, China.
Research Institute of Information Technology, Anhui University of Technology, Ma'anshan, 243000, Anhui, China.
Neural Netw. 2023 Apr;161:55-64. doi: 10.1016/j.neunet.2023.01.039. Epub 2023 Feb 1.
The asynchronous dissipative stabilization for stochastic Markov-switching neural networks (SMSNNs) is investigated. The aim is to design an output-feedback controller with inconsistent mode switching to ensure that the SMSNN is stochastically stable with extended dissipativity. Two situations, which involve completely- and incompletely-known transition rates (TRs), are taken into account. The situation that all TRs are exactly known is considered first. By applying a mode-dependent Lyapunov-Krasovskii functional, Dynkin's formula, and several matrix inequalities, a criterion for the desired performance of the closed-loop SMSNN is derived and a design method for determining the asynchronous controller is developed. Then, the study is generalized to the situation where some TRs are allowed to be uncertain or even fully unknown. An inequality is established for judging the upper bound of the product of the TRs with the Lyapunov matrix by making full use of accessible information on the incompletely-known TRs. Based on the inequality, performance analysis and control synthesis are presented without imposing the zero-sum hypothesis of the uncertainties in the TR matrix. Finally, an example with numerical calculation and simulation is provided to verify the validity of the stabilizing approaches.
研究了随机马尔可夫切换神经网络（SMSNNs）的异步耗散镇定问题。目的是设计一个具有不一致模式切换的输出反馈控制器，以确保SMSNN在扩展耗散性的情况下随机稳定。考虑了两种情况，即转移率（TRs）完全已知和不完全已知。首先考虑所有TRs都精确已知的情况。通过应用与模式相关的李雅普诺夫 - 克拉索夫斯基泛函、 Dynkin公式和几个矩阵不等式，推导了闭环SMSNN期望性能的判据，并开发了一种确定异步控制器的设计方法。然后，将研究推广到一些TRs允许不确定甚至完全未知的情况。通过充分利用关于不完全已知TRs的可获取信息，建立了一个用于判断TRs与李雅普诺夫矩阵乘积上界的不等式。基于该不等式，在不施加TR矩阵不确定性零和假设的情况下进行了性能分析和控制综合。最后，给出了一个带有数值计算和仿真的例子，以验证镇定方法的有效性。
