Uncertain Reaction-diffusion Research Articles

Condition-Based Adaptive Scheme for the Stabilization of an Uncertain Reaction–Diffusion Equation With Nonlinear Dynamic Boundary

Condition-Based Adaptive Scheme for the Stabilization of an Uncertain Reaction–Diffusion Equation With Nonlinear Dynamic Boundary

Integral Sliding Mode Control for a Kind of Impulsive Uncertain Reaction-Diffusion Systems

This article discusses the integral sliding mode control problem for a kind of periodically impulsive uncertain reaction-diffusion systems (IURDSs). A novel integral sliding surface containing impulsive effects and reaction-diffusion terms is constructed, such that the impulsive effects for IURDSs can be removed. A novel sliding mode controller with impulsive effects is designed to ensure the reachability of the specified sliding surface in a finite time interval. By means of linear matrix inequalities (LMIs), the robust exponential stability of this kind of IURDSs are derived. Finally, a numerical example is provided to verify the availability of our findings.

Energy-to-peak synchronization for uncertain reaction-diffusion delayed neural networks

This paper is devoted to energy-to-peak synchronization for uncertain reaction-diffusion delayed neural networks subject to external disturbances. The purpose is to determine a controller in such a way that the drive-response systems not only achieve asymptotical synchronization in the absence of disturbances but also possess a predefined energy-to-peak disturbance-rejection level under zero initial conditions. Through the use of Lyapunov-Krasovskii functionals and various integral inequalities, both delay-independent and dependent conditions are proposed in the form of linear matrix inequalities. When these conditions hold, the needed controller gains can be calculated directly. A numerical example is provided to show the applicability and reduced conservativeness of the present results.

Prescribed-time stabilisation for uncertain reaction-diffusion equations with Neumann boundary control

We study the Neumann boundary feedback stabilisation for reaction-diffusion equations with matched boundary uncertainties (including internal uncertainty and external disturbance) within a prescribed time, where the convergence time is independent of initial conditions and can be prescribed a priori. We first estimate the uncertainties within the prescribed time by constructing an estimator and then propose the prescribed-time boundary control law by utilising backstepping transformation with a time-varying kernel. Neumann boundary control is verified to be uniformly bounded.

Adaptive stabilization for an uncertain reaction–diffusion equation with dynamic boundary condition at control end

This paper is devoted to the stabilization of a class of uncertain reaction–diffusion equations with dynamic boundary condition. Remarkably, the dynamics of boundary condition at control end are considered while unknown parameters are contained in both the intra-domain and the dynamic boundary. This greatly relaxes the restrictions on boundary dynamics and system uncertainties of the related literature where dynamic boundary condition is neglected or considered but unknown parameters are only contained in the dynamic boundary or even completely excluded from the whole system. To solve the control problem, a novel control framework is established by infinite-dimensional backstepping method combining with adaptive compensation technique based on passive identifier. Then, an adaptive state-feedback controller is explicitly constructed which guarantees that all the states of the resulting closed-loop system are bounded while those of the original system converge to zero. A simulation example is provided to validate the effectiveness of the proposed theoretical results.

Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

Passivity and Synchronization of Coupled Uncertain Reaction-Diffusion Neural Networks With Multiple Time Delays.

This paper presents a complex network model consisting of N uncertain reaction-diffusion neural networks with multiple time delays. We analyze the passivity and synchronization of the proposed network model and derive several passivity and synchronization criteria based on some inequality techniques. In addition, by considering the difficulty in achieving passivity (synchronization) in such a network, an adaptive control scheme is also developed to ensure that the proposed network achieves passivity (synchronization). Finally, we design two numerical examples to verify the effectiveness of the derived passivity and synchronization criteria.