Finite-time Control Of Reaction-diffusion Neural Networks In Complex Environments

The purpose of this dissertation is to conduct an in-depth investigation into the key issues within the domain of finite-time control for reaction-diffusion neural networks(RDNNs).Traditional neural networks have ignored temporal and spatial evolution when processing data,leading to limitations in tasks involving spatiotemporal dynamic characteristics.However,these spatiotemporal dynamics are crucial in numerous practical applications.With the rapid advancement of artificial intelligence,the integration of neural networks with the principles of reaction-diffusion systems,known as RDNNs,has garnered widespread attention due to their significant potential in handling complex spatiotemporal data and pattern recognition tasks.In critical domains such as autonomous driving and robotics,it is imperative that RDNNs demonstrate dependable behavior and consistent dynamics,thereby guaranteeing the stability and safety of the systems.Consequently,given the current technological challenges,a deep exploration of the dynamic behavior of RDNNs holds significant importance.Existing research,however,has mainly focused on Lyapunov stability,achieving convergence to equilibrium points as time tends to infinity.From an application perspective,while ensuring system stability,the convergence rate is also an essential performance metric,especially in scenarios with high response time requirements.In comparison,control strategies with finite-time convergence offer advantages.Furthermore,finite-time control possesses stronger disturbance resistance and robustness and provides higher control accuracy.Hence,based on theories such as Lyapunov functional theory,stochastic analysis techniques,and algebraic graph theory,and combined with modern control strategies like event-triggered control and sliding-mode control,this dissertation delves into an in-depth study of the dynamic characteristics of RDNNs in complex environments involving potential impulsive disturbances,cyber attacks,etc.The primary research contents can be summarized as follows:(1)Finite-time fault-tolerant control of stochastic RDNNs in the presence of unknown faults.Chapter 3 addresses the critical issue of system performance degradation caused by real-world challenges such as cyber and physical faults.Firstly,the problem is formulated as convergence estimation and stability analysis of generalized stochastic impulsive systems.Then,a novel method for finite-time stability(FTS)in probability has been developed by utilizing stochastic Lyapunov theory and It?o’s formula.Finally,this analysis is then applied to achieve finite-time fault-tolerant control of stochastic RDNNs.(2)Fixed-time adaptive control of fuzzy RDNNs with discontinuous activation.To handle imprecise and uncertain data effectively,Chapter 4 explores fuzzy RDNNs with fuzzy logic operators.Firstly,the generalized fixed-time stability(Fx TS)criteria and novel integral inequalities are introduced.Then,distributed adaptive control mechanisms are proposed and applied to fuzzy RDNNs under discontinuous activation conditions.Finally,based on the derived fixed-time synchronization criteria,an innovative image encryption algorithm is established.(3)Finite-time sliding mode control of coupled RDNNs with impulsive effects and matched disturbances.In Chapter 5,the control problem of coupled RDNN with multiple nodes cooperating is considered,and the impact of impulses and matched disturbances on system performance is taken into account.Firstly,a novel integral sliding surface function is introduced,and the resulting dynamic of the sliding mode phase is characterized as an impulsive reaction-diffusion system.Then,a finite-time sliding mode control strategy is designed to ensure the finite-time reachability of the sliding surface amidst impulses and matched disturbances.Finally,by means of the piecewise Lyapunov function and the finite-time control approach,the FTS of the dynamic behavior in the sliding mode phase is proven,and the impulses-dependent settling-time strategy is constructed.(4)Fixed-time event-triggered control of multi-cluster coupled RDNNs under hybrid cyber attacks.Chapter 6 focuses on the control problem of multi-cluster coupled RDNNs affected by time-varying transmission delays and hybrid cyber-attacks,encompassing deception and denial-of-service(Do S)attacks.Firstly,employing impulsive and switching signals,the dynamic behavior of coupled RDNN under hybrid cyber-attacks is modeled.Then,a resilient event-triggered control strategy is devised,which combines a time-varying threshold strategy and can avoid Zeno behavior.Meanwhile,the Lyapunov criteria of finite-time convergence and prescribed-set stability are established.Subsequently,the conditions for achieving fixed-time multi-cluster synchronization are derived.Finally,the validity and effectiveness of the proposed results are illustrated by simulation examples.