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

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.

[1]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[2]  Bijnan Bandyopadhyay,et al.  Discrete-time sliding mode control , 2006 .

[3]  B. Bandyopadhyay,et al.  Quasi sliding mode control with quantization in state measurement , 2011, IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society.

[4]  Bijnan Bandyopadhyay,et al.  Output Feedback Sliding-Mode Control for Uncertain Systems Using Fast Output Sampling Technique , 2006, IEEE Transactions on Industrial Electronics.

[5]  Xinghuo Yu,et al.  Discretization behaviors of equivalent control based sliding-mode control systems , 2003, IEEE Trans. Autom. Control..

[6]  Xinghuo Yu,et al.  Discretization Effect on Equivalent Control-Based Multi-Input Sliding-Mode Control Systems , 2008, IEEE Transactions on Automatic Control.

[7]  Xinghuo Yu,et al.  Analysis of Zero-Order Holder Discretization of Two-Dimensional Sliding-Mode Control Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  C. Milosavljevic,et al.  Sampled Data Quasi-Sliding Mode Control Strategies , 2006, 2006 IEEE International Conference on Industrial Technology.

[9]  Susy Thomas,et al.  Reaching law based sliding mode control for discrete MIMO systems , 2010, 2010 11th International Conference on Control Automation Robotics & Vision.

[10]  Maria Letizia Corradini,et al.  Variable structure control of discretized continuous-time systems , 1998, IEEE Trans. Autom. Control..

[11]  Przemyslaw Ignaciuk,et al.  LQ optimal and reaching law-based sliding modes for inventory management systems , 2012, Int. J. Syst. Sci..

[12]  Saif Benjaafar,et al.  A Production-Inventory System With Both Patient and Impatient Demand Classes , 2012, IEEE Transactions on Automation Science and Engineering.

[13]  B. Bandyopadhyay,et al.  The design and Implementation of output feedback based frequency shaped sliding mode controller for the smart structure , 2010, 2010 IEEE International Symposium on Industrial Electronics.

[14]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[15]  Weibing Gao,et al.  Variable structure control of nonlinear systems: a new approach , 1993, IEEE Trans. Ind. Electron..

[16]  B. Draenovi.  The invariance conditions in variable structure systems , 1969 .

[17]  Ulrich W. Thonemann,et al.  Production , Manufacturing and Logistics Analyzing the effect of the inventory policy on order and inventory variability with linear control theory , 2006 .

[18]  A. Bartoszewicz,et al.  Discrete Time Sliding Mode Flow Controller for Multi-source Single-bottleneck Connection-oriented Communication Networks , 2009 .

[19]  G. Golo,et al.  Robust discrete-time chattering free sliding mode control , 2000 .

[20]  Paolo Valigi,et al.  Supply Chain Management by H-Infinity Control , 2008, IEEE Transactions on Automation Science and Engineering.

[21]  Vadim I. Utkin,et al.  Adaptive sliding mode control in discrete-time systems , 1995, Autom..

[22]  Przemyslaw Ignaciuk,et al.  Sliding Mode Dead-Beat Control of Perishable Inventory Systems With Multiple Suppliers , 2012, IEEE Transactions on Automation Science and Engineering.

[23]  Bijnan Bandyopadhyay,et al.  Frequency-Shaped Sliding Mode Control Using Output Sampled Measurements , 2009, IEEE Transactions on Industrial Electronics.

[24]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[25]  S. Janardhanan,et al.  Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach , 2005 .

[26]  Itir Z. Karaesmen,et al.  Managing Perishable and Aging Inventories: Review and Future Research Directions , 2011 .

[27]  B. Drazenovic,et al.  The invariance conditions in variable structure systems , 1969, Autom..

[28]  Christos T. Maravelias,et al.  Integration of control theory and scheduling methods for supply chain management , 2013, Comput. Chem. Eng..

[29]  Christos D. Tarantilis,et al.  Dynamic modeling and control of supply chain systems: A review , 2008, Comput. Oper. Res..

[30]  S. Janardhanan,et al.  Multirate-Output-Feedback-Based LQ-Optimal Discrete-Time Sliding Mode Control , 2008, IEEE Transactions on Automatic Control.

[31]  Bijnan Bandyopadhyay,et al.  High-Performance Tracking Controller for Discrete Plant Using Nonlinear Sliding Surface , 2009, IEEE Transactions on Industrial Electronics.

[32]  Andrzej Bartoszewicz,et al.  Remarks on Discrete-time Variable Structure Control Systems , 1996 .

[33]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[34]  Shailaja Kurode,et al.  Discrete sliding mode control for a class of underactuated systems , 2011, IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society.

[35]  Lizhong Song,et al.  Study of reaching law approach for discrete-time variable structure control system , 2012, 2012 Proceedings of International Conference on Modelling, Identification and Control.

[36]  Andrzej Bartoszewicz,et al.  Discrete-time quasi-sliding-mode control strategies , 1998, IEEE Trans. Ind. Electron..

[37]  Maria Letizia Corradini,et al.  Discrete time sliding mode control of robotic manipulators: Development and experimental validation , 2011, ETFA2011.

[38]  Katsuhisa Furuta,et al.  Variable structure control with sliding sector based on hybrid switching law , 2007 .

[39]  Xinghuo Yu,et al.  Computer-Controlled Variable Structure Systems: The State-of-the-Art , 2012, IEEE Transactions on Industrial Informatics.

[40]  Zidong Wang,et al.  Improved sliding mode control for discrete-time systems via reaching law , 2010 .

[41]  Nicoleta S. Tipi,et al.  Modelling the dynamics of supply chains , 2000, Int. J. Syst. Sci..

[42]  Bijnan Bandyopadhyay,et al.  Multirate Output Feedback Based Robust Quasi-Sliding Mode Control of Discrete-Time Systems , 2007, IEEE Transactions on Automatic Control.

[43]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..