Design of adaptive backstepping congestion controller for ... control problem by the backstepping method

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  • Accepted Manuscript

    Design of adaptive backstepping congestion controller for TCP networks with UDP flows based on minimax

    Zanhua Li, Yang Liu, Yuanwei Jing

    PII: S0019-0578(19)30214-9 DOI: Reference: ISATRA 3200

    To appear in: ISA Transactions

    Received date : 29 July 2018 Revised date : 28 April 2019 Accepted date : 3 May 2019

    Please cite this article as: Z. Li, Y. Liu and Y. Jing, Design of adaptive backstepping congestion controller for TCP networks with UDP flows based on minimax. ISA Transactions (2019),

    This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

  • *Corresponding Author (e-mail:, )

    Design of adaptive backstepping congestion controller for TCP

    networks with UDP flows based on minimax

    Zanhua Li1,2*, Yang Liu1, Yuanwei Jing1*

    1.College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    2.School of science, Shenyang Ligong University, Shenyang, 110168, China

    Abstract: The congestion control problem of TCP network systems with user datagram protocol (UDP) flows is

    investigated in this paper. A nonlinear TCP network model with strict-feedback structure is first established. The

    unknown UDP flow is regarded as the external disturbance, and the maximum UDP flow is calculated by using the

    minimax approach. And then, a congestion control algorithm is proposed by using the adaptive backstepping

    approach. Meanwhile, the adaptive law is employed to estimate the unknown link capacity. The design of the

    adaptive law is to introduce a parameter mapping mechanism to limit the parameter identification range to a

    specified interval, thereby improving the estimation efficiency of the parameters. Furthermore, a state-feedback

    congestion controller is presented to make sure that the output of the system tracks the desired queue. The

    simulation results show the superiority and feasibility of the proposed method.

    Keywords: TCP network; congestion control; minimax; adaptive backstepping technique.

    1 Introduction

    Recently, the active queue management (AQM) has been a very active research area in the internet community

    [1]-[3]. Though there exist a lot of achievements, the congestion control problem based on AQM is still an open

    field. In 2000, Misra et al. [4] established a nonlinear differential equation model for router queues of TCP

    networks based on the fluid-flow theory. Hollot et al. gave a reasonable linearization for the nonlinear dynamic

    model of TCP network in [5]. Authors of [6]-[7] proposed an AQM algorithm based on the proportional integral

    (PI) and proportional differential (PD), respectively. Authors of [8] investigated a robust fractional-order PID

    controller for time-varying parameters of the network system. So far, a number of results have been obtained to

    solve network congestion problems. All the results require the system to be linear. The congestion control

    mechanism of the TCP protocol is considerably complex, in which many nonlinear distortion factors appear.

    Hence, an AQM algorithm was proposed based on the nonlinear network model in [9]. Authors of [10]-[12]

    designed an AQM algorithm by utilizing the fuzzy variable-structure control and neural-networks method,

    respectively. Particle swarm optimization (PSO) was applied to obtain the output weight of radial basis function

    (RBF) neural networks, and then an AQM controller was achieved in [13]. Authors of [14]-[15] considered a

    situation where the external disturbances existed in network systems and an AQM algorithm was presented.

    *Title page showing Author Details

  • It is well known that the backstepping technique is one of the main control methods for nonlinear systems. In

    recent years, this method has been widely used in many fields and a great deal of results have also been obtained

    [16]-[20]. In [16], the backstepping approach was adopted to solve the problem of global uniform asymptotic

    stability for nonlinear systems with an arbitrarily large delay of the input. Authors of [17] investigated the robust

    control problem by the backstepping method for time-delay nonlinear systems with triangular structure, in which

    the system with time-delay was considered. In [18], a robust stabilization issue was studied by using the adaptive

    robust backstepping control method for structure uncertain nonlinear systems in the presence of structured

    uncertainties, external disturbances, and unknown time-varying virtual control coefficients. In [19], a finite-time

    command filtered backstepping approach was proposed for high-order nonlinear systems. Authors of [20]

    designed an optimized backstepping control technique to solve the optimized solutions for the high-order strict-

    feedback systems. In addition, the backstepping technique has been applied to network systems [21]-[23]. In [21],

    the nonlinear output-feedback control algorithm was obtained based on the comparison lemma and backstepping

    technique, and the range of parameters was also proposed. Authors of [22] designed an AQM controller with only

    one output (queue size) measurement, the control law was developed by applying an observer-based backstepping

    design technique. In [23], the prescribed performance, backstepping technique, adaptive control and H∞ control

    were combined to design a congestion controller. Although the research of congestion control strategy has made

    great progress, there are still some problems that have not been fully solved. One of the most important issues is to

    deal with disturbance and the uncertainty in the network system.

    In the existing achievements [24]-[25], on one hand, the disturbance is not considered in the system; on the

    other hand, an assumption that the disturbance has an upper bounded is required and the upper bound is used to

    replace the disturbance. The above two situations can cause certain limitations and conservatism, hence, the idea

    of minimax method is an effective scheme to handle this problem. Compared with the existing ways, the minimax

    control method aims at calculating the disturbance with the worst case, and then discusses the design of controller

    to provide better disturbance rejection characteristics. It is well known that the minimax method is to construct a

    controller to stabilize the system under the case of the worst-case uncertainty. In recent years, the minimax

    method has been applied to many systems [26]-[32]. Authors of [26] proposed minimax guaranteed cost-control

    for uncertain nonlinear systems. Authors of [27] focused on a minimax optimal problem for stochastic systems,

    and the corresponding minimax controller was designed with the worst-case uncertainty. A new minimax control

    method was proposed by using universal learning networks in [28]. Authors in [29] used a linear minimax

    observer to study the problem of sliding-mode control design for linear systems with incomplete and noisy

    measurements of the output and exogenous disturbances. Authors of [30] dealt with the robust and non-fragile

    minimax control problem for a T-S model including the parametric uncertainty terms of the nonlinear systems. A

    robust minimax linear quadratic gaussian (LQG) controller was designed based on an uncertain system model,

    which was constructed by measuring the plant variations and modeling the error between the measured and

    modelled frequency-responses in [31]. A stochastic minimax optimal time-delay state feedback control strategy

    for uncertain quasi-integrable Hamiltonian systems was proposed in [32]. The minimax method was also applied

    recently to AQM computer network, which was a kind of typical nonlinear systems with the nonlinear structure

    and time-varying parameters. Authors of [33]-[34] proposed an AQM controller for linearized congestion router

    network systems in the presence of unknown time-varying link number and disturbances based on the idea of

  • minimax method.

    On the other hand, the adaptive technique was an efficient method for the uncertain systems [35]. Therefore, in

    order to handle unknown network situations, some researchers adopted adaptive control methods. Authors of [36]

    designed a controller, which can adapt to unknown or slowly varying parameters by using the feedback

    linearization and the backstepping technique. An adaptive generalized minimum variance congestion controller

    was proposed in [37] based on active queue management (AQM) strategy. Sun et al. [38] gave an adaptive

    proportional-integral controller, which was robust with respect to non-responsive flows. In order to overcome the

    drawback of the Generalized Minimum Variance method, authors of [39] proposed a wavelet neural network