Research On Finite-time Synchronization Control Of T-S Fuzzy Discrete Complex Networks

Complex networks are composed of a large number of dynamic nodes and parallel paths,which is an effective tool to describe the topological structure and dynamic properties of various complex systems.In recent years,discrete complex networks have attracted much attention due to their potential advantages in digital simulation and computation,especially the synchronization problem has broad application prospects in signal and information processing,industrial Internet and robot control.The traditional Lyapunov asymptotic stability only focuses on the dynamic trajectory and control performance of the system in the infinite-time interval,while the finite-time stability can reflect the transient performance of the system in the finite-time interval.Therefore,it is of great value to analyze the synchronization behavior of discrete complex networks in the finite-time frame.In addition,the complexity of the network environment will inevitably lead to a variety of constraints and interference,which is easy to cause adverse effects on the actual control effect.Accordingly,combined with T-S fuzzy model,this paper investigates the finite-time synchronization control problem of discrete complex networks.The main research contents are given as follows:The finite-time synchronization control problem of T-S fuzzy discrete complex networks with varying time delay is discussed.A generalized discrete complex network is established under the IF-THEN rule of T-S fuzzy model,which extends the existing continuous time model.In order to effectively reduce the consumption of communication resources,an adaptive event-triggered method based on dynamic threshold parameters is proposed,and a fuzzy pinning controller is further designed to realize the global control of the network by controlling part of the nodes.Lyapunov-Krasovskii functional is constructed to analyze the synchronization error system,and sufficient criteria for finite-time synchronization are obtained.Results of two simulation examples verify the validity of the proposed control strategy.For T-S fuzzy Markov jumping discrete complex networks with partial mode transition probability,the finite-time H_∞synchronization problem with mixed delay and actuator faults is analyzed.Considering the bandwidth limitation and the fact that the system state is difficult to obtain directly,the fault-tolerant synchronization controller based on the measured output of the sensor is designed by using quantization technique.Meanwhile,the controller uses asynchronous signals generated by hidden Markov model to reduce the dependence on the direct system modes.A modal dependent stability analysis framework is established,and the conditions are given to ensure that the closed-loop synchronization error system is bounded by mean square finite-time and has specified H_∞performance.Finally,the simulation of two systems is used to proved the feasibility of the designed control method.Aiming at the uncertainties of parameters and the security threats caused by network attacks in complex networks,a non-fragile fuzzy control method is proposed.Based on the previous study of the homogeneous Markov jumping model,a T-S fuzzy discrete complex network model following the piecewise non-homogeneous Markov process is constructed,where the mode transition probability is described by a convex polyhedron structure.By analyzing the double-mode related Lyapunov-Krasovskii functional,sufficient conditions are obtained for finite-time boundness of the synchronization error system,and then the control effectiveness is proved in attacked Lorenz chaotic systems.Based on the previous research,semi-Markov model is used to model the system mode evolution,and the finite-time strictly dissipative synchronization control problem is further studied for T-S fuzzy discrete complex networks with random packet loss.In order to reduce the burden of network communication,a distributed dynamic event triggering mechanism is presented to restrain the frequency of information update.For random packet loss sequence in sensor to controller channels,an equivalent model is used to compensate synchronization error information and fuzzy controller is designed.In the process of Lyapunov stability analysis,a set of sufficient criteria based on linear matrix inequalities are obtained via introducing delay-dependent augmentation terms and improved reciprocally convex matrix inequality technique.Simulation results show the effectiveness and practicability of the proposed method.