School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China.
School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China.
ISA Trans. 2023 Jul;138:442-450. doi: 10.1016/j.isatra.2023.03.023. Epub 2023 Mar 22.
This study addresses the asynchronous control problem for a semi-Markov switching system in the presence of singular perturbation and an improved triggering protocol. To decrease the occupation of network resources, an improved protocol is skillfully established by adopting two auxiliary offset variables. Unlike the existing protocols, the established improved protocol is capable of arranging information transmission with more degrees of freedom, thereby reducing the communication frequency and maintaining control performance. Apart from the reported hidden Markov model, a nonhomogeneous hidden semi-Markov model is used to handle the mode mismatch between the systems and controllers. Benefiting from Lyapunov techniques, parameter-dependent sufficient conditions are devised to ensure a stochastically stable subject to a predetermined performance. Finally, the validity and practicability of the theoretical results are verified via a numerical example and a tunnel diode circuit model.
本研究针对存在奇异摄动和改进触发协议的半马尔可夫切换系统的异步控制问题进行了研究。为了减少网络资源的占用，通过采用两个辅助偏移变量，巧妙地建立了改进协议。与现有协议不同，所建立的改进协议能够以更多的自由度安排信息传输，从而降低通信频率并保持控制性能。除了已报道的隐马尔可夫模型外，还使用非齐次隐半马尔可夫模型来处理系统和控制器之间的模式不匹配问题。利用李雅普诺夫技术，设计了参数依赖的充分条件，以确保在预定性能下的随机稳定性。最后，通过数值示例和隧道二极管电路模型验证了理论结果的有效性和实用性。
