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Robust control of LTI systems over unreliable communication channels with unreliable acknowledgments

机译：带有不可靠确认的不可靠通信信道上的LTI系统的鲁棒控制

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We consider the robust (H∞) control problem for linear time-invariant systems over unreliable communication channels that are subject to packet losses from sensors to the controller and from the controller to the actuators. Moreover, the acknowledgments of control packet transmissions are also sent over reverse unreliable communication channels, which is known as the quasi-TCP model. The robust control problem is formulated within a stochastic zero-sum dynamic game framework, from which we obtain an H∞ controller that minimizes the worst-case cost function in the presence of an adversary in the dynamical system. We characterize a set of existence conditions of the H∞ controller in terms of the disturbance attenuation parameter γ and packet loss rates. For the least disturbance attenuation scenario (as γ → 8), we show that the H∞ control system converges to the corresponding LQG system. We also show that the H∞ controller for the TCP- and UDP-cases can be arrived at as appropriate limits of the solution for the quasi-TCP problem. Numerical examples are presented to illustrate the theoretical results.
机译：我们考虑了不可靠通信信道上线性时不变系统的鲁棒（H∞）控制问题，该通信信道易受传感器到控制器以及控制器到执行器的数据包丢失的影响。而且，控制分组传输的确认也通过反向不可靠的通信信道发送，这被称为准TCP模型。随机零和动态博弈框架内提出了鲁棒控制问题，从中我们获得了H∞控制器，该控制器使在动态系统中存在敌手的情况下的最坏情况成本函数最小化。我们根据扰动衰减参数γ和丢包率来表征H∞控制器的一组存在条件。对于最小的干扰衰减情形（如γ→8），我们表明H∞控制系统收敛到相应的LQG系统。我们还表明，可以将针对TCP和UDP情况的H∞控制器作为拟TCP问题解决方案的适当限制。数值例子说明了理论结果。

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