**Sliding Mode Congestion Controller for**

** Data Transmission Networks with Unknown and**

** Variable Packet Loss Rates**

**Andrzej BARTOSZEWICZ, Paweł LATOSIŃSKI **

Łódź University of Technology, Institute of Automatic Control,

Stefanowskiego 18/22, 90-942 Łódź, Poland

andrzej.bartoszewicz@p.lodz.pl

* * Corresponding author*

**Abstract: **In this paper, the problem of data flow control in multi-source connection oriented communication networks is considered. Each source in the considered networks is characterized by its own maximum transmission rate. Furthermore, data packets sent by the sources are transferred through lossy links and some of them can be lost before arriving at a common bottleneck node. The amount of data lost during the transmission is not known, but upper bounded for each source. If at some time the bottleneck link cannot transfer all arriving data, then the excess data is stored in a buffer with limited capacity. In order to eliminate data losses caused by the buffer overflow and to ensure full utilization of the available bandwidth, in this paper a new non-switching type reaching law for discrete time sliding mode control systems is proposed and applied to design a congestion controller for the networks.

**Keywords: **Communication Networks, Reaching Law Approach, Discrete-Time Sliding Mode Control.

**>>Full text<<
CITE THIS PAPER AS: **Andrzej BARTOSZEWICZ, Paweł LATOSIŃSKI,

**Sliding Mode Congestion Controller for Data Transmission Networks with Unknown and Variable Packet Loss Rates**,

*Studies in Informatics and Control*, ISSN 1220-1766, vol. 25(1), pp. 109-121, 2016.

**Introduction**

Continuous time sliding mode controllers were introduced in Russia in late 1950s [1,2]. Soon, they have proved to be computationally efficient, easy to tune and insensitive with respect to a class of external disturbances and model uncertainties [3]. These highly desirable properties made them very attractive for the control engineering community [4-7]. The classical method of designing a sliding mode controller consists of stating the control law and proving that it ensures stability of the sliding motion. However, digital implementation of this control may result in undesirable chattering, i.e. high frequency oscillations that may cause energy loss or plant damage. In order to prevent this effect, discrete time sliding mode controllers were developed in 1980s [8,9].

The introduction of discrete time quasi-sliding modes led to many further advances in the field [10-21]. Furuta proposed an algorithm that drives the system state to a cone-like sector defined in the state space [10]. An alternative method introduced by Gao et. al. in [11] drives the state strictly to a vicinity of the sliding hyperplane, rather than to some sector. That work presents the switching type discrete time sliding mode control, i.e. it requires the control strategy to drive the system state to the other side of the switching surface in each consecutive sampling instant. On the other hand, the equivalent control method used by Bartolini et. al. [12] drives the state to a certain neighbourhood of the sliding hyperplane without the need to cross the manifold in every sampling instant. This non-switching type discrete time sliding mode control was then studied by Bartoszewicz [13]. The width of the boundary layer in this case was further considered by Su et. al. [14]. Afterwards, an integral sliding mode control strategy has also been proposed in order to eliminate the reaching phase in discrete time sliding mode control [15]. An exhaustive review of the discrete time sliding mode control literature can be found in paper [16].

One of the main drawbacks of the sliding mode control methodology is the need for full information about the system state at the moment of calculating the control signal. Since this requirement often limits the applicability of such strategies, various authors have worked on that problem. Corradini and Orlando utilized the concept of time-delay control to estimate the effects of uncertainties in the switching region [17]. Bandyopadhyay and Janardhanan proposed a novel method called multirate output feedback approach [18], in which each value of the control signal is calculated based on multiple output samples. The approach was further discussed in papers [19-21].

In early years of sliding mode control, the design procedure included proving stability of the sliding motion by finding an appropriate Lyapunov function. However, that stage can be circumvented by utilizing an alternative method of sliding mode controller design called the reaching law approach. This approach, first proposed in [22] for continuous time systems and in [11] for discrete time ones (see [23] for further analysis), is based on stating the desired evolution of the sliding variable and applying the evolution to synthesize a feasible control law. Various authors have proposed new control methods based on the reaching law approach [24-28], which greatly improved upon the classic equivalent control or the constant-plus-proportional reaching law introduced by Gao et. al. [11]. The case of mismatched disturbance has also been considered in several works [29-31].

In recent years, the area of broadband connectivity has experienced rapid growth. Consequently, the increase of traffic intensity in data transmission networks highlighted the importance of efficient congestion control. Since the physical channel capacity does not grow as fast as the bandwidth demand, it became vital to implement new data transfer solutions. This area of research has been investigated by various authors [32-46]. An overview of earlier congestion control strategies is presented in [32]. Then, the problem of source rate synchronization present in several of the earlier algorithms has been tackled in [33]. Furthermore, an extensive new approach to flow rate controller design was proposed in [34]. In the same work, novel stochastic algorithms for data transmission networks have been proposed. Furthermore, various researchers at that time proposed strategies based on the classical PD controllers [35], PID controllers [36], adaptive methods [37] or fuzzy PID controllers [38].

An important issue that arises in congestion control of data transmission networks is the presence of long propagation delays. To address this problem, many authors have employed control schemes based on a Smith predictor. First, Mascolo introduced an algorithm that uses the difference between the queue length and its demand value as well as the number of ‘in flight’ packets to calculate the flow rate. This method was initially applied to a simplified case with a single virtual connection [39] and then extended to networks consisting of multiple connections [40]. Then, a method combining the Smith predictor with the PI controller was proposed [41] and shown to reduce the average bottleneck queue length. The idea of combining the Smith predictor with a proportional controller with saturation was further explored by De Cicco et. al. [42].

In recent years, several researchers have utilized sliding mode control to regulate the data flow in communication networks. Bartoszewicz and Żuk proposed to model the data transmission networks as discrete time systems with the available bandwidth acting as the disturbance [43]. In the same work, an algorithm ensuring a finite time response of the system was presented. Afterwards, various authors utilized discrete-time integral sliding mode control [44, 45], which offers good robustness at the price of relative complexity of controller design. Baburaj and Bandyopadhyay further proposed a simplified approach based on deriving a first order model of the network and applying a method based on equivalent sliding mode control [46]. An extensive review of congestion control techniques can be found in [30].

In this paper, data flow in communication networks will be regulated by means of reaching law based sliding mode control. The main contribution of such an approach is providing good robustness with respect to unpredictable bit rate variations and packet losses, while ensuring a computationally efficient controller operation. In contrast to a similar approach proposed in [30], the method introduced in this paper does not require the packet losses to be *a priori* known or constant. The networks considered in this work consist of several data sources and a common bottleneck link. Data sent from the sources is queued at the bottleneck link up to a certain maximum value determined by the buffer capacity. The objective of the control strategy is to ensure that the buffer capacity is never exceeded and that the available bandwidth is always fully utilized. Furthermore, the control signal should neither require the sources to send a negative amount of data, nor to exceed their maximum transmission capabilities. The upper and lower bounds of the control signal and the bottleneck queue length will be ensured by an appropriate choice of the design parameters. This will be achieved in the presence of mismatched uncertainty, which appears in the discrete model of the network.

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