Reaching Law Approach to the Sliding Mode Control of Periodic Review Inventory Systems

Abstract

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. Note to Practitioners-This paper presents a new periodic reviewinventory management strategy which prevents from exceeding the available storage capacity, ensures smooth order evolution and helps attenuate the bullwhip effect. The strategy is scalable, computationally efficient, and easy to implement in any typical inventory replenishment system. The strategy explicitly accounts for transportation losses and different lead times of commodity suppliers.

Disturbance Observer-Based Adaptive Tracking Control With Actuator Saturation and Its Application

“…If actuator saturation is ignored in the design, the ARC controller can handle both parametric uncertainty by adaptive control and unstructure uncertainty via deterministic robust feedback control and integrate these two control techniques in a unified form by using a projection-based adaptive law. Based on (9), the resulting ARC controller can be given by (11) By substituting (11) into (9), we have (12) where is the regressor for parameter adaptation. Noting Assumption 2 and P1 in (6), the robust function is then chosen to satisfy the following robust performance conditions [20]: (13) where is a positive design parameter that can be arbitrarily small.…”

“…Then, one smooth example of satisfying (13) is given by (14) where can be regarded as a nonlinear feedback gain, is any smooth function satisfying , where and is the upper bound of . Lemma 1: Consider the parameter estimates updated by the projection-type adaptation law (4), and the adaptation function in (5) is chosen as and defining , thus, the ARC law (11) guarantees that all signals are bounded. Furthermore, the positive-definite function defined by is bounded by .…”

“…It seems that the control problem with uncertainties has been solved by the ARC controller (11). However, this controller might not work very well in practice.…”

“…Meanwhile, by borrowing ideas from the ARC [5], [16] and to avoid employing large feedback gains in practical implementations. An approach that based on disturbance observer has been applied for systems to compensate the strong effects of disturbances [11]- [15]. Motivated by the observation, in this paper, a novel terminal sliding-mode-based nonlinear disturbance observer (TSDO), where the modeling inaccuracy and disturbance are integrated into a lumped disturbance, is designed to estimate the lump disturbances acting on the system.…”

The problem of state constraints in designing the discrete time sliding mode controller

“…Originally, the reaching law method was introduced for continuous time systems [19], and then developed for discrete time ones [20]. Recently, a large number of new reaching laws were presented [21][22][23][24][25][26][27][28][29][30].…”