Inverse Tangent Reaching Law for Discrete Sliding Mode Control with Application to Inventory Management

In this paper we propose a modified, non-switching type reaching law for quasi-sliding mode control of linear discrete time dynamic systems. The reaching law determines the sliding variable rate of change proportional to the negative value of the inverse tangent of this variable. The approach proposed in this work helps satisfy input and state constraints in the controlled system, and at the same time it does not excessively damp the system convergence rate when the sliding variable is small. In the second part of this paper the proposed reaching law is successfully applied to solve the periodic review inventory management problem, with suppliers' constraints explicitly taken into account.