基于积分滑模控制的非理想变时滞神经网络有限时间同步
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摘要
研究一类非理想变时滞神经网络的有限时间同步问题.首先,利用驱动-响应概念推导误差系统,并运用同步误差构造一个合适的积分滑模流型,若误差系统的状态轨迹在有限时间内到达滑模面,则同步误差将随其后在有限时间内收敛于零.然后,结合神经元激活函数的约束条件,设计一种合适的滑模控制器,根据所设计的控制器和Lyapunov稳定性理论,误差系统的状态轨迹能够在有限时间内到达滑模面,从而非理想变时滞神经网络的有限时间同步能够实现.最后,通过数值仿真结果验证所提出设计方法的有效性.
The finite-time synchronization problem of a class of nonidentical neural networks with time-varying delay is studied. Firstly, by using the drive-response concept to derive an error system, a suitable integral sliding mode manifold is constructed by applying the synchronization error. If the state trajectories of the error system are driven onto the sliding mode surface, the synchronization error will thereafter converge to zero in finite time. Then, by combining the bounded conditions on neuron activation functions, a proper sliding mode controller is designed. Based on the designed controller and the Lyapunov stability theory, the state trajectories of the error system can be driven onto the sliding mode surface,such that the finite-time synchronization of nonidentical neural networks with time-varying delay can be performed.Finally, numerical simulation results verify the effectiveness of the proposed method.
The finite-time synchronization problem of a class of nonidentical neural networks with time-varying delay is studied. Firstly, by using the drive-response concept to derive an error system, a suitable integral sliding mode manifold is constructed by applying the synchronization error. If the state trajectories of the error system are driven onto the sliding mode surface, the synchronization error will thereafter converge to zero in finite time. Then, by combining the bounded conditions on neuron activation functions, a proper sliding mode controller is designed. Based on the designed controller and the Lyapunov stability theory, the state trajectories of the error system can be driven onto the sliding mode surface,such that the finite-time synchronization of nonidentical neural networks with time-varying delay can be performed.Finally, numerical simulation results verify the effectiveness of the proposed method.
引文
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[26]Li S,Zhou M,Yu X.Design and implementation of terminal sliding mode control method for PMSMspeed regulation system[J].IEEE Trans on Industrial Informatics,2013,9(4):1879-1891.
[27]Yang J,Li S,Yu X.Sliding-mode control for systems with mismatched uncertainties via a disturbances observer[J].IEEE Trans on Industrial Electronics,2013,60(1):160-169.
[28]张庆超,马瑞卿.无刷直流电机转速伺服系统反步高阶滑模控制[J].控制与决策,2016,31(6):961-968.(Zhang Q C,Ma R Q.Backstepping high order sliding mode control for brushless DC motor speed servo control system[J].Control and Decision,2016,31(6):961-968.)
[29]Zhang H G,Ma T D,Huang G B,et al.Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control[J].IEEE Trans on Systems,Man,and Cybernetics-Part B:Cybernetics,2010,40(3):831-844.
[2]Li T,Song A G,Fei S M,et al.Synchronization control of chaotic neural networks with time-varying and distributed delays[J].Nonlinear Analysis,2009,71(5):2372-2384.
[3]Lam H K.Chaotic synchronization using output/full state-feedback polynomial controller[J].IET Control Theory and Applications,2010,4(11):2285-2292.
[4]Gan Q.Synchronization of chaotic neural networks with unknown parameters and random time-varying delays based on adaptive sampled-data control and parameter identification[J].IET Control Theory and Applications,2012,6(10):1508-1515.
[5]Rakkiyappan R,Dharani S,Cao J D.Synchronization of neural networks with control packet loss and time-varying delay via stochastic sampled-data controller[J].IEEETrans on Neural Networks and Learning Systems,2015,26(12):3215-3226.
[6]Gan Q T,Xu R,Kang X B.Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification[J].Nonlinear Dynamics,2012,67(3):1893-1902.
[7]Wang L M,Shen Y,Yin Q,et al.Adaptive synchronization of memrisor-based neural networks with time-varying delays[J].IEEE Trans on Neural Networks and Learning Systems,2015,26(9):2033-2042.
[8]Li J M,He C,Zhang W Y,et al.Adaptive synchronization of delayed reaction-diffusion neural networks with unknown non-identical time-varying coupling strengths[J].Neurocomputing,2017,219:144-153.
[9]Li X D,Song S J.Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method[J].Communications in Nonlinear Science and Numerical Simulation,2014,19(10):3892-3900.
[10]Chen W H,Lu X M,Zheng W X.Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks[J].IEEE Trans on Neural Networks and Learning Systems,2015,26(4):734-748.
[11]Chen W H,Luo S X,Zheng W X.Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption[J].IEEE Trans on Neural Networks and Learning Systems,2016,27(12):2696-2710.
[12]Li X,Rakkiyappan R.Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays[J].Communications in Nonlinear Science and Numerical Simulation,2013,18(6):1515-1523.
[13]Fang Y,Yang K,Li K.Synchronization of chaotic delayed neural networks via impulsive control[J].J of Applied Mathematics,2014,DOI:10.1155/2014/305264.
[14]Zhang G D,Shen Y.Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control[J].Neural Networks,2014,55:1-10.
[15]Huang H,Feng G.Synchronization of nonidentical chaotic neural networks with time delays[J].Neural Networks,2009,22(7):869-874.
[16]Zhang D,Xu J.Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller[J].Applied Mathematics and Computation,2010,217(1):164-174.
[17]Gan Q T,Xu R,Yang P H.Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(1):433-443.
[18]Shi Y,Zhu P,Qin K.Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller[J].Neurocomputing,2014,123:443-459.
[19]Yu X,Man Z.Fast terminal sliding-mode control design for nonlinear dynamical systems[J].IEEE Trans on Circuits and Systems-I:Fundamental Theory and Applications,2002,49(2):261-264.
[20]Xu R,OzgunerU.Sliding mode control of a class of underactuated systems[J].Automatica,2008,44(1):233-241.
[21]Feng Y,Yu X,Man Z.Non-singular terminal sliding mode control of rigid manipulators[J].Automatica,2002,38(12):2159-2167.
[22]Xiong J J,Zheng E H.Position and attitude tracking control for a quadrotor UAV[J].ISA Trans,2014,53(3):725-731.
[23]Zheng E H,Xiong J J,Luo J L.Second order sliding mode control for a quadrotor UAV[J].ISA Trans,2014,53(4):1350-1356.
[24]Xiong J J,Zhang G B.Global fast dynamic terminal sliding mode control for a quadrotor UAV[J].ISA Trans,2017,66(1):233-240.
[25]刘锦涛,吴文海,李静,等.四旋翼无人机SO(3)滑模变结构姿态控制器设计[J].控制与决策,2016,31(6):1057-1064.(Liu J T,Wu W H,Li J,et al.Sliding mode variable structure attitude controller design of quadrotor UAVs on SO(3)[J].Control and Decision,2016,31(6):1057-1064.)
[26]Li S,Zhou M,Yu X.Design and implementation of terminal sliding mode control method for PMSMspeed regulation system[J].IEEE Trans on Industrial Informatics,2013,9(4):1879-1891.
[27]Yang J,Li S,Yu X.Sliding-mode control for systems with mismatched uncertainties via a disturbances observer[J].IEEE Trans on Industrial Electronics,2013,60(1):160-169.
[28]张庆超,马瑞卿.无刷直流电机转速伺服系统反步高阶滑模控制[J].控制与决策,2016,31(6):961-968.(Zhang Q C,Ma R Q.Backstepping high order sliding mode control for brushless DC motor speed servo control system[J].Control and Decision,2016,31(6):961-968.)
[29]Zhang H G,Ma T D,Huang G B,et al.Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control[J].IEEE Trans on Systems,Man,and Cybernetics-Part B:Cybernetics,2010,40(3):831-844.