Event-Based Impulsive Control of Continuous-Time Dynamic Systems and Its Application to Synchronization of Memristive Neural Networks

This paper investigates exponential stabilization of continuous-time dynamic systems (CDSs) via event-based impulsive control (EIC) approaches, where the impulsive instants are determined by certain state-dependent triggering condition. The global exponential stability criteria via EIC are derived for nonlinear and linear CDSs, respectively. It is also shown that there is no Zeno-behavior for the concerned closed loop control system. In addition, the developed event-based impulsive scheme is applied to the synchronization problem of master and slave memristive neural networks. Furthermore, a self-triggered impulsive control scheme is developed to avoid continuous communication between the master system and slave system. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed event-based impulsive controllers.

[1]  Wei Zhang,et al.  Synchronization of Memristor-Based Coupling Recurrent Neural Networks With Time-Varying Delays and Impulses , 2015, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[4]  V. Costanza,et al.  Deterministic impulse control in native forest ecosystems management , 1990 .

[5]  Daoyi Xu,et al.  Robust stability of uncertain impulsive control systems with time-varying delay , 2007, Comput. Math. Appl..

[6]  Tingwen Huang,et al.  Event-Triggering Sampling Based Leader-Following Consensus in Second-Order Multi-Agent Systems , 2015, IEEE Transactions on Automatic Control.

[7]  David J. Hill,et al.  Comparison Principle and Stability of Discrete-Time Impulsive Hybrid Systems , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[9]  Yao-Lin Jiang,et al.  Anti-synchronization and intermittent anti-synchronization of two identical hyperchaotic Chua systems via impulsive control , 2015 .

[10]  Bin Liu,et al.  Exponential stability via event-triggered impulsive control for continuous-time dynamical systems , 2014, Proceedings of the 33rd Chinese Control Conference.

[11]  Karl-Erik Årzén,et al.  A simple event-based PID controller , 1999 .

[12]  Jun Wang,et al.  Global Exponential Synchronization of Multiple Memristive Neural Networks With Time Delay via Nonlinear Coupling , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[13]  M. R. Vonder,et al.  Asynchronous measurement and control: a case study on motor synchronization , 1999 .

[14]  Zhong-Ping Jiang,et al.  Event-Based Leader-following Consensus of Multi-Agent Systems with Input Time Delay , 2015, IEEE Transactions on Automatic Control.

[15]  Athanasios V. Vasilakos,et al.  Differential Evolution With Event-Triggered Impulsive Control , 2015, IEEE Transactions on Cybernetics.

[16]  Donghua Zhou,et al.  Event-Based Recursive Distributed Filtering Over Wireless Sensor Networks , 2015, IEEE Transactions on Automatic Control.

[17]  SERGEY DASHKOVSKIY,et al.  Input-to-State Stability of Nonlinear Impulsive Systems , 2012, SIAM J. Control. Optim..

[18]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

[19]  Manuel Mazo,et al.  Decentralized Event-Triggered Control Over Wireless Sensor/Actuator Networks , 2010, IEEE Transactions on Automatic Control.

[20]  Wei Xing Zheng,et al.  Impulsive Stabilization and Impulsive Synchronization of Discrete-Time Delayed Neural Networks , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Sun Zhijie,et al.  Event-e-ISS for discrete-time impulsive dynamical networks , 2015, 2015 34th Chinese Control Conference (CCC).

[22]  Richard E. Bellman.  Asymptotic series for the solutions of linear differential-difference equations , 1958 .

[23]  Wei Zhang,et al.  Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control , 2016, Neurocomputing.

[24]  Ju H. Park,et al.  Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities , 2015, Appl. Math. Comput..

[25]  Guodong Zhang,et al.  New Algebraic Criteria for Synchronization Stability of Chaotic Memristive Neural Networks With Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[26]  Qi Li,et al.  Event-triggered synchronization control for complex networks with uncertain inner coupling , 2015, Int. J. Gen. Syst..

[27]  Michael Z. Q. Chen,et al.  Event-based synchronisation of linear discrete-time dynamical networks , 2015 .

[28]  Zhigang Zeng,et al.  Exponential Adaptive Lag Synchronization of Memristive Neural Networks via Fuzzy Method and Applications in Pseudorandom Number Generators , 2014, IEEE Transactions on Fuzzy Systems.

[29]  Tingwen Huang,et al.  Globally exponential stability of delayed impulsive functional differential systems with impulse time windows , 2016 .

[30]  Gang Feng,et al.  Distributed event-triggered control of multi-agent systems with combinational measurements , 2013, Autom..

[31]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

[32]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

[33]  Yasuhiro Masutani,et al.  Flyaround maneuvers on a satellite orbit by impulsive thrust control , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[34]  Jinde Cao,et al.  Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Jinde Cao,et al.  Pth Moment Exponential Stochastic Synchronization of Coupled Memristor-based Neural Networks with Mixed Delays via Delayed Impulsive Control , 2015, Neural Networks.

[36]  Karl Henrik Johansson,et al.  Event-based broadcasting for multi-agent average consensus , 2013, Autom..

[37]  David J. Hill,et al.  Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks , 2015, Neural Networks.

[38]  W. P. M. H. Heemels,et al.  Periodic Event-Triggered Control for Linear Systems , 2013, IEEE Trans. Autom. Control..

[39]  Gang Feng,et al.  Self-Triggered Consensus for Multi-Agent Systems With Zeno-Free Triggers , 2015, IEEE Transactions on Automatic Control.

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

[41]  Zhong-Ping Jiang,et al.  Event-based consensus of multi-agent systems with general linear models , 2014, Autom..

[42]  Jan Lunze,et al.  A state-feedback approach to event-based control , 2010, Autom..

[43]  Wei Zhu,et al.  Global impulsive exponential synchronization of time-delayed coupled chaotic systems , 2008 .

[44]  R. Rakkiyappan,et al.  Impulsive controller design for exponential synchronization of delayed stochastic memristor-based recurrent neural networks , 2016, Neurocomputing.