Summary In this paper, a novel reaching law for discrete‐time variable structure systems is proposed. It ensures that the representative point (state) of the controlled plant approaches the switching plane in finite time and then crosses it in every subsequent step. Moreover, the proposed reaching law ensures that for the nominal plant the absolute value of the sliding variable asymptotically decreases to zero, and for the perturbed plant, it converges to a smaller interval around zero than with the application of previously proposed reaching laws. The control method proposed in this paper guarantees asymptotic stability of the nominal system and uniform ultimate boundedness of the perturbed one. Furthermore, the method ensures that the sliding variable rate of change (i.e. the difference between its values at any two subsequent sampling instants) is bounded by design parameters, which do not depend on the system initial conditions. This is a highly desirable property, as it results in a priori specified, ‘almost’ constant convergence rate of the sliding variable when the system state is far off the switching plane and helps enforce state constraints in the system. Copyright © 2014 John Wiley & Sons, Ltd.

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This paper presents the first attempt to design a reaching law-based discrete-time sliding mode controller with a relative degree 2 switching variable. The current value of this variable is only affected by the control signal and disturbance generated two time instants ago. It is demonstrated that the new reaching law-based strategy offers a smaller quasi-sliding mode band width when compared to a similar control scheme with relative degree 1 switching variable. This in turn leads to reduced system output error in the control system proposed in the paper.

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Reaching-law-based discrete sliding mode controllers are well known to be easy to tune and robust with respect to disturbance. In recent years, it has been demonstrated that their robustness can be further enhanced with the use of arbitrary relative degree sliding variables. However, reaching laws using such variables only ensure a good sliding mode performance of the system when the perturbations affecting the plant are matched, which is a very restrictive assumption. To address this issue and to further improve robustness of the plant, in this article, we propose a new model reference approach for strategies with relative degree two sliding variables. In the proposed approach, the reaching law is first used to control the evolution of a disturbance-free model of the plant, and then, the original system state is driven toward that of the model with a secondary controller. It will be shown that the proposed approach ensures better system robustness compared to the conventional reaching law approach and that it does not require the assumption about matched uncertainties.

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.