# CCAIB: Congestion Control Based on Adaptive Integral Backstepping for Wireless Multi-Router Network
###### Abstract
[42; 43; 44; 45] use a model with changing RTT to design controllers. Backstepping sliding mode control is used in [46]. Ref. [47] applies Hoo control and integral backstepping to a model with both internal and external disturbances. The Transmission Control Protocol (TCP) Vegas model is used in [48]. Ref. [49] incorporates funnel control and fuzzy logic into backstepping method. All the above research is related to a single congestion router. However, data travels through multiple routers to the receiving end in the real networks, and with the increase in data traffic on the internet, simultaneous congestion of multiple routers is common. Ref. [50] proves that congestion control algorithms designed for single bottleneck router networks are not feasible in multiple bottleneck routers networks. Multiple bottleneck routers are considered in very few studies. Refs. [51; 52] use Linear Matrix Inequality (LMI) to study the stability of the networks in which congestion occurs on multiple routers. However, network congestion is a typical nonlinear problem. Besides, all the above algorithms are proposed for wired internet, which believe all packet loss is caused by congestion. This is false in wireless networks because packet loss can also occur in the wireless links. When packet loss occurs in the wireless link, the congestion control algorithms for wired networks may assume that congestion occurs mistakenly, thus causing excessive packet loss in the queue. Ref. [53] introduces a wireless network model by modifying the fluid model, and then gives a Hoo method after approximate linearization. After that, a few pieces of research emerged based on the new model. Fractional order proportional integral and small signal theory are used in [54]. Ref. [55] proposes a linear quadratic method to deal with the wireless AQM problem. [PERSON]. [56] extends the backstepping control strategy to wireless TCP network to solve the AQM problem. It is anticipated that data traffic of mobile internet will grow exponentially, which will create congestion in wireless networks on multiple routers. However, as far as the authors know, existing algorithms designed for wireless networks congestion control are based on approximate linearized models, which are distortion compared to the actual networks. Besides, to the best of our knowledge, there is little few research on wireless networks with congestion occurring on multiple routers. The main contributions of this paper can be summarized as follows. 1. A wireless network model is introduced, in which a serial topology is considered and the interrelationships between connecting routers is formulated. 2. The adaptive control theory is applied to estimate the packet loss ratios of the uplink and downlink. Based on the estimation, a novel congestion control algorithm called CCAIB is designed using the integral backstepping procedure. Different from the previous work for wired networks, the packet loss ratios of the wireless links are taken into account. 3. Comparison is conducted between CCAIB and H\(\infty\) in the performance of queue length stability, window size and packet loss ratio in the queue. 4. The influence of network parameters such as link capacity, propagation delay, wireless packet loss ratios, desired queue length and router location on the performance of CCAIB are analyzed. The rest of this paper is arranged as follows. In Section 2, the topology and mathematical model of wireless networks is given. The controller design process is described in Section 3. Performance evaluation is carried out in Section 4. A conclusion is given in Section 5.