# CCAIB: Congestion Control Based on Adaptive Integral Backstepping for Wireless Multi-Router Network
###### Abstract  
Wireless information collecting and processing terminals, such as cell phones, sensors and smart wearable devices, are expected to be deployed on a large scale in the future to promote the continuous advancement of the global information revolution. Since most of these terminals connect to each other using long-distance and high-speed networks by multiple routers and eventual access the internet, the application of mobile internet is gradually increasing and data traffic on the mobile internet is growing exponentially, from which arises congestion in wireless networks on multiple routers. This research solves the congestion problem for wireless networks with multiple bottleneck routers. First, the wireless network model is expanded to multi-router networks, which considers the interrelationships between connecting routers. Afterwards, a new Active Queue Management (AQM) method called Congestion Control Based on Adaptive Integral Backstepping (CCAIB) is designed to handle congestion in wireless networks. In CCAIB, an adaptive control method is used to estimate the packet loss ratios of wireless links and a controller is designed based on the estimation results through a backstepping procedure. It can be shown from the simulation results that the performance of CCAIB is better than the Hoo algorithm in queue length stability. Besides, the window size of CCAIB is 100 times that of the Hoo algorithm, and the proportion of packets marked as discarded when using CCAIB is about 0.1% of the Hoo algorithm. Moreover, CCAIB has satisfactory adaptability to network parameters such as wireless link capacity, propagation delay, wireless packet loss ratios, desired queue length and router location. congestion control; wireless networks; adaptive integral backstepping  
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limitations such as blindness, passiveness, and delay. For the above reasons, control methods deployed on routers are advised by Internet Engineering Task Force (IETF) [7]. The Random Early Detection (RED) algorithm [8] discards new packets with a certain ratio when the queue length is over a certain value. Afterwards, a series of improved algorithms of RED are proposed [9; 10; 11; 12; 13; 14; 15]. However, the performance of the RED algorithms vary greatly when different parameters are selected [16]. In order to achieve more stable performance, [PERSON] proposed an algorithm to achieve fairer congestion control by controlling queue delay rather than queue length [17]. For the same purpose, [PERSON] introduced a new algorithm, which can adjust the parameters adaptively [18]. After the fluid model [19] is proposed, some new router-based control algorithms [20; 21; 22], are applied to congestion control. Many of them are adopted in the control design of AQM mechanisms to handle the changing and uncertainty of the network parameters. Ref. [23] focuses on link capacity variance and model uncertainty. Topology uncertainty is considered in [24]. Some researchers use advanced control design methods, such as neural networks control [25], fuzzy control [26], predictive control [27; 28; 29] and so on. In addition to the above-mentioned algorithms based on the control methods, [PERSON] [30], [PERSON] [31] and [PERSON] [32] introduce optimization theory to solve the congestion problem. Backstepping is a typical control design method for nonlinear systems [33; 34; 35; 36; 37; 38], which designs a controller for nonlinear systems in two steps. Lyapunov functions are designed for each step and the two steps are connected by a virtual control law. Backstepping is commonly used in complex systems and it has been widely used in AQM for the last few years. Ref. [39] combines backstepping, Hoo, adaptive control and prescribed performance control (PPC) to design a queue tracking controller. In [40], minimax together with integral backstepping is used, which considers user datagram protocol (UDP) flows as disturbances. Input and output saturations are both noted in [41]. Ref.