具有随机采样和数据丢失的线性离散遥操作系统的稳定性分析
Stability analysis of the linear discrete teleoperation systems with stochastic sampling and data dropout
摘要：
本文讨论了在一般通信网络上由连续时间主、从、操作员和环境组成的具有离散时间控制器的采样数据遥操作系统的稳定性条件。从机器人和主机器人的输出信号被量化与随机采样周期被建模为是从一个有限的集合。应用输入延迟法，将概率采样系统转化为系统矩阵中含有随机参数的连续时间系统。本文的主要贡献是推导了线性离散遥操作系统的不太保守的稳定性条件，考虑到随机采样率，恒定的时间延迟和数据包丢失的可能性等挑战。辍学人数是由有限状态马尔可夫链驱动的。首先，问题的最大采样周期，保持稳定的下限制定。这个问题被构造成一个凸优化规划的线性矩阵不等式（LMI）。其次，基于李雅普诺夫-克拉索夫斯基方法，提出了闭环采样数据双边遥操作系统的随机和指数稳定性的充分条件。该准则考虑了采样时间对系统稳定性和透明性的影响，并对采样时间、控制增益和机器人阻尼进行了限制。忽视这项研究会破坏遥操作系统的稳定性和透明度。数值仿真结果被用来验证所提出的稳定性准则，并说明采样结构的有效性。
英文摘要：
This paper addresses the stability conditions of the sampled-data teleoperation systems consisting continuous time master, slave, operator, and environment with discrete time controllers over general communication networks. The output signals of the slave and master robots are quantized with stochastic sampling periods which are modeled as being from a finite set. By applying an input delay method, the probabilistic sampling system is converted into a continuous-time system including stochastic parameters in the system matrices. The main contribution of this paper is the derivation of the less conservative stability conditions for linear discrete teleoperation systems taking into account the challenges such as the stochastic sampling rate, constant time delay and the possibility of data packet dropout. The numbers of dropouts are driven by a finite state Markov chain. First, the problem of finding a lower bound on the maximum sampling period that preserves the stability is formulated. This problem is constructed as a convex optimization program in terms of linear matrix inequalities (LMI). Next, Lyapunov Krasovskii based approaches are applied to propose sufficient conditions for stochastic and exponential stability of closed-loop sampled-data bilateral teleoperation system. The proposed criterion notifies the effect of sampling time on the stability transparency trade-off and imposes bounds on the sampling time, control gains and the damping of robots. Neglecting this study undermines both the stability and transparency of teleoperation systems. Numerical simulation results are used to verify the proposed stability criteria and illustrate the effectiveness of the sampling architecture.
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