Communication time delays in a bilateral teleoperation system often carries a stochastic nature, particularly when we have multiple masters or slaves. In this paper, we tackle the problem for a single-master multislave (SMMS) teleoperation system by assuming an asymmetric and semi-Markovian jump protocol for communication of the slaves with the master under time-varying transition rates. A nonlinear robust controller is designed for the system that guarantees its global robust ${H_{\infty}} $ stochastic stability in the sense of the Lyapunov theory. Employing the nonlinear feedback linearization technique, the dynamics of the closed-loop teleoperator is decoupled into two interconnected subsystems: 1) master–slave tracking dynamics (coordination) and 2) multislave synchronization dynamics. Employing an improved reciprocally convex combination technique, the stability analysis of the closed-loop teleoperator is conducted using the Lyapunov–Krasovskii methodology, and the stability conditions are expressed in the form of linear matrix inequalities that can be solved efficiently using numerical algorithms. Numerical studies and simulation results validate the effectiveness of the proposed controller design algorithm in both tracking and synchronization performance of the SMMS system, and robustly handling the stochastic and nondifferentiable nature of communication delays.

中文翻译：

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具有半马尔可夫跳跃随机间隔时变时延通信信道的单主多从系统的双边遥操作

双边远程操作系统中的通信时间延迟通常具有随机性，尤其是当我们有多个主设备或从设备时。在本文中，我们通过假设一个不对称且半马尔可夫跳跃协议来解决随时间变化的从机与主机之间的通信，从而解决了单主机多从机（SMMS）远程操作系统的问题。为系统设计了非线性鲁棒控制器，以保证其在Lyapunov理论意义上的全局鲁棒$ {H _ {\ infty}} $随机稳定性。利用非线性反馈线性化技术，闭环遥操作器的动力学被解耦为两个相互关联的子系统：1）主从跟踪动力学（协调）和2）多从同步动力学。采用改进的往复凸组合技术，使用Lyapunov–Krasovskii方法对闭环遥操作器进行稳定性分析，并以线性矩阵不等式的形式表示稳定性条件，可以使用数值算法对其进行有效求解。数值研究和仿真结果验证了所提出的控制器设计算法在SMMS系统的跟踪和同步性能方面的有效性，并能可靠地处理通信时延的随机性和不可微分性。