In this brief a new switching type reaching law for sliding mode control of discrete time systems is proposed. The proposed reaching law is a refined version of an earlier approach (introduced in the seminal work of Gao et al.) which enforces constant plus proportional decrease rate of change of the sliding variable. In our method, the proportional term is modified, so that the rate is always bounded and decreases slower for smaller values of the sliding variable than in the original approach. The refined reaching law proposed in this brief, on the one hand, ensures faster convergence and better robustness of the controlled plant than the earlier approach, and on the other hand, it helps satisfy constraints of important signals in the system. Furthermore, in the latter part of this brief a new nonswitching type reaching law is introduced, and it is demonstrated that it results in further improvement of the system robustness without increasing the magnitude of the critical signals in the system.

In this paper, a discrete-time sliding mode inventory management strategy based on a novel non-switching type reaching law is introduced. The proposed reaching law eliminates undesirable chattering, and ensures that the sliding variable rate of change is upper bounded by a design parameter which does not depend on the system initial conditions. This approach guarantees fast convergence with non-negative, upper limited supply orders, and ensures that the maximum stock level may be specified a priori by the system designer. Furthermore, a sufficient condition for 100% customers' demand satisfaction is derived. The inventory replenishment system considered in this paper involves multiple suppliers with different lead times and different transportation losses in the delivery channels.

In this study, a new reaching law for sliding mode control of discrete time systems is proposed and applied to solve the problem of congestion avoidance in multi‐source, connection oriented data transmission networks. Since the proposed reaching law does not require switching of the sliding variable between positive and negative values in each successive control step, it leads to chattering free operation, does not cause overshoots and helps achieve 100% exploitation of the bottleneck link available bandwidth. Furthermore, the proposed controller always generates bounded data transmission rates. The rates are limited by design parameters and they do not depend on the network initial conditions. The properties of the proposed controller are stated as three theorems, formally proved and verified in a simulation example.

In this article, a new optimal model-based sliding mode controller is proposed and applied to a perishable inventory system. The sliding variable of the real plant is forced to follow the reference trajectory generated by the model of the plant. This model is controlled by a linear quadratic (LQ) optimal controller. The control structure proposed in this article allows on one hand to maintain the advantages of the optimal controller, such as limiting and smoothing out the initial control signal, which, in the considered scenario, is the replenishment order sent to the suppliers. On the other hand, once the model converges to the vicinity of the desired state, the sliding mode controller can react significantly faster to the unknown disturbance, i.e., consumers' demand. Since the reference trajectory is unperturbed by the disturbance, this allows to combine the advantages of both approaches: limited and smooth initial control signal and good robustness in the quasi-steady state. Those properties are analytically demonstrated, as well as in computer simulations.

The employment of input filters in modern DC–DC converters is mandatory in order to ensure EMC (Electro-Magnetic Compatibility), provide power electronics with decent voltage and minimize the converter influence on the power grid. The LC type input filters bring also a possibility of voltage and current oscillation that may occur in the system. This oscillation may rise to a certain level that affects system stability. A wide range of methods are employed in order to attenuate these oscillations and allow appropriate system transient response. In this paper, the sliding mode control (SMC) strategy is proposed to reduce the input LC filter voltage and current oscillation and allow DC (Direct Current) output voltage control for both resistive and constant power load. The proposed control algorithm is intended for use in railway, tram and trolleybus DC/DC converters. For the proposed scheme of control simulation, a model is developed using Simulink software. Furthermore, laboratory stand experiments are carried out to verify simulation results.

The reaching law approach comprises of first specifying the required evolution of the sliding variable. Then, a sliding mode controller that enforces this evolution is designed. The main advantage of this method with respect to “classical” sliding mode control is better control of the plant dynamics and state constraints during the reaching phase. In this paper, a review of a number of new works on reaching laws for discrete time systems is presented. The differences and similarities between them are discussed.