Finite-Time Decentralized Control of IT2 T–S Fuzzy Interconnected Systems With Discontinuous Interconnections

This paper investigates the finite-time decentralized control problem for interconnected systems with discontinuous interconnections. By using the interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model, a unified IT2 T–S fuzzy interconnected system is provided, in which the global system is described as a fuzzy blending of local subsystems under IF-THEN rules. In addition, based on the differential inclusion theory, the solutions of such discontinuous system are defined in the sense of Filippov. In order to stabilize the considered system in finite time, several decentralized discontinuous state feedback controllers are proposed. Furthermore, by the finite-time stabilization theory and generalized Lyapunov functional method, decentralized control is carried out and several sufficient criteria are derived to ensure the finite-time stabilization of the concerned system. Correspondingly, the settling times for stabilization are given. Finally, the proposed methodology is illustrated by an example.

[1]  Qiang Wang,et al.  A novel design framework for smart operating robot in power system , 2018, IEEE/CAA Journal of Automatica Sinica.

[2]  Wen-June Wang,et al.  Stability and stabilization of fuzzy large-scale systems , 2004, IEEE Transactions on Fuzzy Systems.

[3]  V. Haimo.  Finite time controllers , 1986 .

[4]  W. Haddad,et al.  Finite-time stabilization of nonlinear impulsive dynamical systems☆ , 2008 .

[5]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[6]  Jerry Mendel,et al.  Type-2 Fuzzy Sets and Systems: An Overview [corrected reprint] , 2007, IEEE Computational Intelligence Magazine.

[7]  Hongbin Zhang,et al.  Delay-dependent decentralised H α filtering for fuzzy interconnected systems with time-varying delay based on Takagi¿Sugeno fuzzy model , 2013 .

[8]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[9]  Guang-Hong Yang,et al.  Decentralized State Feedback Control of Uncertain Affine Fuzzy Large-Scale Systems With Unknown Interconnections , 2016, IEEE Transactions on Fuzzy Systems.

[10]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Yun Ho Choi,et al.  Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems , 2016, IEEE Transactions on Cybernetics.

[12]  Xin-Ping Guan,et al.  Finite/Fixed-Time Stabilization for Nonlinear Interconnected Systems With Dead-Zone Input , 2017, IEEE Transactions on Automatic Control.

[13]  Guang-Hong Yang,et al.  Adaptive decentralized control for a class of interconnected nonlinear systems via backstepping approach and graph theory , 2017, Autom..

[14]  Daniel W. C. Ho,et al.  Finite-Time Cluster Synchronization of T–S Fuzzy Complex Networks With Discontinuous Subsystems and Random Coupling Delays , 2015, IEEE Transactions on Fuzzy Systems.

[15]  Xinzhi Liu,et al.  Finite-Time Stability of Large-Scale Systems with Interval Time-Varying Delay in Interconnection , 2017, Complex..

[16]  Jin Zhao,et al.  Via and return path discontinuity impact on high speed digital signal quality , 2000, IEEE 9th Topical Meeting on Electrical Performance of Electronic Packaging (Cat. No.00TH8524).

[17]  Hak-Keung Lam,et al.  Polynomial Fuzzy-Model-Based Control Systems: Stability Analysis Via Piecewise-Linear Membership Functions , 2011, IEEE Transactions on Fuzzy Systems.

[18]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Lynne E. Parker,et al.  Multiple Mobile Robot Systems , 2008, Springer Handbook of Robotics.

[20]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[21]  Kok Kiong Tan,et al.  Decentralized control design for large-scale systems with strong interconnections using neural networks , 2003, IEEE Trans. Autom. Control..

[22]  Huaguang Zhang,et al.  Novel Switching Jumps Dependent Exponential Synchronization Criteria for Memristor-Based Neural Networks , 2017, Neural Processing Letters.

[23]  Wassim M. Haddad,et al.  Finite-time stabilization of nonlinear impulsive dynamical systems , 2007, 2007 European Control Conference (ECC).

[24]  Jinhui Zhang,et al.  Decentralized adaptive controller design for large-scale power systems , 2015 .

[25]  Magdi S. Mahmoud,et al.  Decentralized Control and Filtering in Interconnected Dynamical Systems , 2010 .

[26]  M.R. Iravani,et al.  Power Management Strategies for a Microgrid With Multiple Distributed Generation Units , 2006, IEEE Transactions on Power Systems.

[27]  Shuping He,et al.  Finite-time sliding mode control design for a class of uncertain conic nonlinear systems , 2017, IEEE/CAA Journal of Automatica Sinica.

[28]  Changchun Hua,et al.  Model Following Controller Design for Large-Scale Systems With Time-Delay Interconnections and Multiple Dead-Zone Inputs , 2011, IEEE Transactions on Automatic Control.

[29]  Hongbin Zhang,et al.  Asynchronous H∞ fuzzy control for a class of switched nonlinear systems via switching fuzzy Lyapunov function approach , 2016, Neurocomputing.

[30]  Guodong Zhang,et al.  Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Marius-F. Danca,et al.  Chaotifying Discontinuous Dynamical Systems via Time-Delay Feedback Algorithm , 2004, Int. J. Bifurc. Chaos.

[32]  Peter Xiaoping Liu,et al.  Adaptive Fuzzy Decentralized Control for a Class of Strong Interconnected Nonlinear Systems With Unmodeled Dynamics , 2018, IEEE Transactions on Fuzzy Systems.

[33]  Dragoslav D. Šiljak,et al.  Decentralized control of complex systems , 2012 .

[34]  Sheng-Dong Xu,et al.  Robustness Design of Fuzzy Control for Nonlinear Multiple Time-Delay Large-Scale Systems via Neural-Network-Based Approach , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[35]  Jin Bae Park,et al.  Decentralized Sampled-Data Fuzzy Observer Design for Nonlinear Interconnected Systems , 2016, IEEE Transactions on Fuzzy Systems.

[36]  Zhanshan Wang,et al.  Exponential Stabilization of Memristive Neural Networks via Saturating Sampled-Data Control , 2017, IEEE Transactions on Cybernetics.

[37]  Yongming Li,et al.  Observer-Based Adaptive Decentralized Fuzzy Fault-Tolerant Control of Nonlinear Large-Scale Systems With Actuator Failures , 2014, IEEE Transactions on Fuzzy Systems.

[38]  Cheng-Wu Chen,et al.  Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control , 2005, IEEE Trans. Fuzzy Syst..

[39]  F. M. Moukam Kakmeni,et al.  Chaos control and duration time of a class of uncertain chaotic systems , 2003 .

[40]  Xin-Ping Guan,et al.  Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties , 2016, Autom..

[41]  T.C. Green,et al.  Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid , 2007, IEEE Transactions on Power Electronics.

[42]  Lihong Huang,et al.  Novel Adaptive Control and State-Feedback Control Strategies to Finite-Time Stabilization of Discontinuous Delayed Networks , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[43]  Lei Guo,et al.  Decentralized output-feedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures , 2016, Autom..

[44]  Guang-Hong Yang,et al.  Neural-Network-Based Adaptive Decentralized Fault-Tolerant Control for a Class of Interconnected Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[45]  Qiuye Sun,et al.  Quasi-Z-Source Network-Based Hybrid Power Supply System for Aluminum Electrolysis Industry , 2017, IEEE Transactions on Industrial Informatics.

[46]  Bo Zhao,et al.  Decentralized Control for Large-Scale Nonlinear Systems With Unknown Mismatched Interconnections via Policy Iteration , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[47]  Qiuye Sun,et al.  Optimal Placement of Energy Storage Devices in Microgrids via Structure Preserving Energy Function , 2016, IEEE Transactions on Industrial Informatics.

[48]  S. Bhat,et al.  Finite-time stability of homogeneous systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[49]  Zhou Gu,et al.  An adaptive event‐triggering scheme for networked interconnected control system with stochastic uncertainty , 2017 .

[50]  Xiangpeng Xie,et al.  Observer-Based Non-PDC Control for Networked T–S Fuzzy Systems With an Event-Triggered Communication , 2017, IEEE Transactions on Cybernetics.

[51]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[52]  Dan Ye,et al.  A cooperative detection and compensation mechanism against Denial-of-Service attack for cyber-physical systems , 2018, Inf. Sci..