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Design of Feedback Controls Supporting TCP Based on the State-Space Approach

机译：基于状态空间的支持TCP的反馈控制设计

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This paper investigates how to design feedback controls supporting transmission control protocol (TCP) based on the state-space approach for the linearized system of the well-known additive increase multiplicative decrease (AIMD) dynamic model. We formulate the feedback control design problem as state-space models without assuming its structure in advance. Thereby, we get three results that have not been observed by previous studies on the congestion control problem. 1) In order to fully support TCP, we need a proportional-derivative (PD)-type state-feedback control structure in terms of queue length (or RTT: round trip time). This backs up the conjecture in the networking literature that the AQM RED is not enough to control TCP dynamic behavior, where RED can be classified as a P-type AQM (or as an output feedback control for the linearized AIMD model). 2) In order to fully support TCP in the presence of delays, we derive delay-dependent feedback control structures to compensate for delays explicitly under the assumption that RTT, capacity and number of sources are known, where all existing AQMs including RED, REM/PI and AVQ are delay-independent controls. 3) In an attempt to interpret different AQM structures in a unified manner rather than to compare them via simulations, we propose a PID-type mathematical framework using integral control action. As a performance index to measure the deviation of the closed-loop system from an equilibrium point, we use a linear quadratic (LQ) cost of the transients of state and control variables such as queue length, aggregate rate, jitter in the aggregate rate, and congestion measure. Stabilizing gains of the feedback control structures are obtained minimizing the LQ cost. Then, we discuss the impact of the control structure on performance using the PID-type mathematical framework. All results are extended to the case of multiple links and heterogeneous delays.
机译：本文研究了如何基于状态空间方法为著名的加性乘增减（AIMD）动态模型的线性系统设计支持传输控制协议（TCP）的反馈控制。我们将反馈控制设计问题表述为状态空间模型，而无需事先假设其结构。从而，我们获得了先前关于拥塞控制问题的研究未曾观察到的三个结果。 1）为了完全支持TCP，我们需要一种基于队列长度（或RTT：往返时间​​）的比例微分（PD）型状态反馈控制结构。这支持了网络文献中的猜测，即AQM RED不足以控制TCP动态行为，其中RED可以归类为P型AQM（或归类为线性化AIMD模型的输出反馈控件）。 2）为了在存在延迟的情况下完全支持TCP，我们推导了依赖于延迟的反馈控制结构，以在已知RTT，容量和源数目的前提下明确补偿延迟，其中所有现有AQM（包括RED，REM / PI和AVQ是与延迟无关的控件。 3）为了试图以统一的方式解释不同的AQM结构，而不是通过仿真进行比较，我们提出了一种使用积分控制作用的PID型数学框架。作为衡量闭环系统与平衡点之间偏差的性能指标，我们使用状态和控制变量（例如队列长度，总速率，总速率抖动，和拥塞措施。获得了反馈控制结构的稳定增益，从而使LQ成本降至最低。然后，我们使用PID型数学框架讨论控制结构对性能的影响。所有结果都扩展到多个链接和异构延迟的情况。

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