A Simplify Type Reduction for Interval Type-2 Fuzzy Sliding Controllers

In this paper, a new reduction approach is presented to simplify the type reduction procedure for an interval type-2 fuzzy sliding controller. An interval type-2 fuzzy set can be considered as a collection of a large number type-1 fuzzy set. The union and intersection of all type-1 fuzzy sets with the corresponding embedded membership functions being their membership functions are found. With the information represented by the union and intersection combined, a type-1 membership function is retrieved and an interval type-2 fuzzy set is reduced to be a type-1 fuzzy set. The proposed simplified type reduction approach is also applied to the design of a hybrid interval type-2 fuzzy sliding controller for a ball-and-beam system. Compared to Extended-Karnik-Mendel (EKM) type reduction method, the simulation results are included to show the effectiveness of the designed hybrid interval type-2 fuzzy sliding controllers using the simplified type reduction.

[1]  M. Melgarejo,et al.  A Fast Recursive Method to Compute the Generalized Centroid of an Interval Type-2 Fuzzy Set , 2007, NAFIPS 2007 - 2007 Annual Meeting of the North American Fuzzy Information Processing Society.

[2]  Hung-Liang Cheng,et al.  Digital Integral Action in Variable Structure Control with Fuzzy Logic for DC-to-AC Converters , 2012 .

[3]  Chin-Wang Tao,et al.  Fuzzy Swing-Up and Fuzzy Sliding-Mode Balance Control for a Planetary-Gear-Type Inverted Pendulum , 2009, IEEE Transactions on Industrial Electronics.

[4]  Jerry M. Mendel,et al.  Enhanced Karnik--Mendel Algorithms , 2009, IEEE Transactions on Fuzzy Systems.

[5]  Chin-Wang Tao,et al.  Robust fuzzy control for a plant with fuzzy linear model , 2005, IEEE Transactions on Fuzzy Systems.

[6]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

[7]  Vicente Milanés Montero,et al.  On-line learning of a fuzzy controller for a precise vehicle cruise control system , 2013, Expert Syst. Appl..

[8]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[9]  Miguel A. Melgarejo,et al.  A comparative study between two algorithms for computing the generalized centroid of an interval type-2 fuzzy set , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[10]  M. Melgarejo,et al.  Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[11]  Jerry M. Mendel,et al.  Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems , 2002, IEEE Trans. Fuzzy Syst..

[12]  Pei-Jun Lee,et al.  A Fuzzy Control Based Robotic Fish with Multiple Actuators , 2012 .

[13]  Yeong-Hwa Chang,et al.  Fuzzy Sliding-Mode Formation Control for Multirobot Systems: Design and Implementation , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Chuen-Chien Lee.  FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[15]  Chih-Min Lin,et al.  Type-2 fuzzy controller design using a sliding-mode approach for application to DC-DC converters , 2005 .

[16]  Hani Hagras,et al.  A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots , 2004, IEEE Transactions on Fuzzy Systems.

[17]  Jeffrey Tweedale,et al.  Fuzzy control loop in an autonomous landing system for Unmanned Air Vehicles , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[18]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems , 1989 .

[19]  Naoyuki Kubota,et al.  Adaptive formation behaviors of multi-robot for cooperative exploration , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[20]  Chin-Wang Tao,et al.  Fuzzy sliding-mode control for ball and beam system with fuzzy ant colony optimization , 2012, Expert Syst. Appl..

[21]  Mao-Hsiung Chiang,et al.  Intelligent Pitch Control for a 2MW Wind Turbine , 2012 .

[22]  H. Hagras,et al.  Type-2 FLCs: A New Generation of Fuzzy Controllers , 2007, IEEE Computational Intelligence Magazine.