Event‐triggered H∞ control for a class of nonlinear networked control systems using novel integral inequalities

This paper is concerned with event‐triggered H∞ control for a class of nonlinear networked control systems. An event‐triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event‐triggered transmission scheme, the closed‐loop system is modeled as a system with an interval time‐varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov–Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event‐triggered H∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to the robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality‐based conditions are formulated to design both event‐triggered and time‐triggered H∞ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[2]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[3]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[4]  F. Fairman,et al.  Nonlinear H∞ control: a J-dissipative approach , 1997, IEEE Trans. Autom. Control..

[5]  D. Siljak,et al.  Robust stabilization of nonlinear systems: The LMI approach , 2000 .

[6]  T. Başar.  Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses , 2001 .

[7]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[8]  Long Wang,et al.  Robust stabilization of nonlinear sampled-data systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[9]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[10]  Qing-Long Han,et al.  Robust $H_{\infty}$ Control for Uncertain Takagi–Sugeno Fuzzy Systems With Interval Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

[11]  Paulo Tabuada,et al.  Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks , 2007, IEEE Transactions on Automatic Control.

[12]  C. Peng,et al.  State feedback controller design of networked control systems with interval time‐varying delay and nonlinearity , 2008 .

[13]  Qing-Long Han,et al.  A New $H_{{\bm \infty}}$ Stabilization Criterion for Networked Control Systems , 2008, IEEE Transactions on Automatic Control.

[14]  Xiaofeng Wang,et al.  Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability , 2009, IEEE Transactions on Automatic Control.

[15]  N. Zheng,et al.  Fuzzy $H_{\infty}$ Tracking Control for Nonlinear Networked Control Systems in T–S Fuzzy Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Qing-Long Han,et al.  A Delay Decomposition Approach to H1 Control of Networked Control Systems , 2009, Eur. J. Control.

[17]  Mo-Yuen Chow,et al.  Networked Control System: Overview and Research Trends , 2010, IEEE Transactions on Industrial Electronics.

[18]  Min Wu,et al.  Absolute stability and stabilization for Lurie networked control systems , 2011 .

[19]  Peng Shi,et al.  A new approach to network-based H∞ control for stochastic systems , 2012 .

[20]  Dong Yue,et al.  A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems , 2013, IEEE Transactions on Automatic Control.

[21]  Qing-Long Han,et al.  A Novel Event-Triggered Transmission Scheme and ${\cal L}_{2}$ Control Co-Design for Sampled-Data Control Systems , 2013, IEEE Transactions on Automatic Control.

[22]  Huajing Fang,et al.  H∞ static output feedback control for nonlinear networked control systems with time delays and packet dropouts. , 2013, ISA transactions.

[23]  Jenq-Lang Wu.  Robust H∞ control for polytopic nonlinear control systems , 2013, IEEE Transactions on Automatic Control.

[24]  Dong Yue,et al.  Event-based fault detection for networked systems with communication delay and nonlinear perturbation , 2013, J. Frankl. Inst..

[25]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[26]  Songlin Hu,et al.  L2 ‐Gain analysis of event‐triggered networked control systems: a discontinuous Lyapunov functional approach , 2013 .

[27]  Qing-Long Han,et al.  Event-triggered dynamic output feedback control for networked control systems , 2014 .

[28]  Baolin Zhang,et al.  Network-based modelling and active control for offshore steel jacket platform with TMD mechanisms , 2014 .

[29]  Qing-Long Han,et al.  A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems , 2014, Autom..

[30]  Magdi S. Mahmoud,et al.  Networked feedback control for nonlinear systems with random varying delays , 2014, J. Frankl. Inst..

[31]  Dong Yue,et al.  Event-triggered tracking control for discrete-time multi-agent systems , 2014, IMA J. Math. Control. Inf..

[32]  Shuli Sun,et al.  Observer‐based H ∞  control for networked systems with bounded random delays and consecutive packet dropouts , 2014 .

[33]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[34]  Qing-Long Han,et al.  On designing network-based H ∞ controllers for stochastic systems , 2015 .

[35]  Zhong-Ping Jiang,et al.  A Small-Gain Approach to Robust Event-Triggered Control of Nonlinear Systems , 2015, IEEE Transactions on Automatic Control.

[36]  Qing-Long Han,et al.  Network-Based Output Tracking Control for a Class of T-S Fuzzy Systems That Can Not Be Stabilized by Nondelayed Output Feedback Controllers , 2015, IEEE Transactions on Cybernetics.

[37]  Kun Liu,et al.  Discrete‐time network‐based control under scheduling and actuator constraints , 2015 .

[38]  Dong Yue,et al.  Decentralized control of network‐based interconnected systems: A state‐dependent triggering method , 2015 .

[39]  Li Qiu,et al.  H∞ control of networked control systems based on Markov jump unified model , 2015 .

[40]  Zhong-Ping Jiang,et al.  A survey of recent results in quantized and event-based nonlinear control , 2015, International Journal of Automation and Computing.

[41]  Karl Henrik Johansson,et al.  Networked Control With Stochastic Scheduling , 2015, IEEE Transactions on Automatic Control.

[42]  Kun Liu,et al.  Networked Control Systems in the Presence of Scheduling Protocols and Communication Delays , 2014, SIAM J. Control. Optim..

[43]  Qing-Long Han,et al.  Network-Based Fault Detection Filter and Controller Coordinated Design for Unmanned Surface Vehicles in Network Environments , 2016, IEEE Transactions on Industrial Informatics.

[44]  Qing-Long Han,et al.  A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs , 2016, IEEE Transactions on Cybernetics.

[45]  Xinghuo Yu,et al.  Survey on Recent Advances in Networked Control Systems , 2016, IEEE Transactions on Industrial Informatics.

[46]  Baolin Zhang,et al.  Event-triggered H∞ reliable control for offshore structures in network environments , 2016 .

[47]  Qing-Long Han,et al.  Distributed networked control systems: A brief overview , 2017, Inf. Sci..