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Stabilization of Networked Multi-Input Systems With Channel Resource Allocation

机译：具有通道资源分配的网络化多输入系统的稳定化

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In this paper, we study the problem of state feedback stabilization of a linear time-invariant (LTI) discrete-time multi-input system with imperfect input channels. Each input channel is modeled in three different ways. First it is modeled as an ideal transmission system together with an additive norm bounded uncertainty, introducing a multiplicative uncertainty to the plant. Then it is modeled as an ideal transmission system together with a feedback norm bounded uncertainty, introducing a relative uncertainty to the plant. Finally it is modeled as an additive white Gaussian noise channel. For each of these models, we properly define the capacity of each channel whose sum yields the total capacity of all input channels. We aim at finding the least total channel capacity for stabilization. Different from the single-input case that is available in the literature and boils down to a typical $ {cal H}_{infty} $ or $ {cal H}_{2}$ optimal control problem, the multi-input case involves allocation of the total capacity among the input channels in addition to the design of the feedback controller. The overall process of channel resource allocation and the controller design can be considered as a case of channel-controller co-design which gives rise to modified nonconvex optimization problems. Surprisingly, the modified nonconvex optimization problems, though appear more complicated, can be solved analytically. The main results of this paper can be summarized into a universal theorem: The state feedback stabilization can be accomplished by the channel-controller co-design, if and only if the total input channel capacity is greater than the topological entropy of the open-loop system.
机译：在本文中，我们研究了具有不完善输入通道的线性时不变（LTI）离散时间多输入系统的状态反馈稳定问题。每个输入通道都以三种不同的方式建模。首先，将其建模为理想的传动系统，以及加性范数有界的不确定性，从而将乘法不确定性引入工厂。然后将其建模为理想的传输系统，以及反馈范围界定的不确定性，从而为工厂引入相对不确定性。最后，将其建模为加性高斯白噪声通道。对于这些模型中的每一个，我们都正确定义每个通道的容量，其总和得出所有输入通道的总容量。我们旨在找到最少的稳定总信道容量。与文献中提供的单输入案例不同，归结为典型的$ {cal H} _ {infty} $或$ {cal H} _ {2} $最优控制问题，多输入案例涉及除了反馈控制器的设计外，还可以在输入通道之间分配总容量。信道资源分配和控制器设计的整个过程可以视为信道控制器协同设计的一种情况，这会引起修改后的非凸优化问题。出人意料的是，尽管修改后的非凸优化问题看起来更为复杂，但仍可以通过分析来解决。本文的主要结果可以归纳为一个通用定理：当且仅当总输入通道容量大于开环的拓扑熵时，才可以通过通道控制器协同设计来实现状态反馈稳定化。系统。

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