Discrete time sliding mode inventory management — Hyperbolic tangent reaching law based approach

In this paper a novel non-switching type reaching law for quasi-sliding mode control of linear discrete time systems is proposed. The reaching law determines the sliding variable rate of change proportional to the negative value of the hyperbolic tangent of this variable. The approach proposed in this paper helps satisfy input and state constraints in the controlled system, and at the same time it does not unduly damp the system convergence rate in the vicinity of the sliding plane. In the second part of this paper we apply the proposed reaching law to solve the periodic review inventory management problem, with suppliers´ constraints explicitly taken into account.