Fault-Tolerant Sampled-Data Fuzzy Control For Nonlinear Parabolic PDE Systems

In practice,many physical processes are essentially characterized by spatial distribution,which can usually be described by parabolic partial differential equation（PDE）.Their states are not only related to time but also depend on spatial location,such as temperature distribution,fluid process,reaction-diffusion process and so on.Meanwhile,nonlinear phenomena widely appears in practical engineering systems,and fuzzy control as a simple and effective control method is widely used to control nonlinear systems.With the rapid development of digital technology and computer,sampled-data control has attracted much attention because of its advantages of high efficiency,high reliability and low cost.What’s more,faults may occur in the practical process,which will cause system performance deterioration or even instability.Therefore,it is necessary and meaningful to study the problem of fault-tolerant sampled-data fuzzy control for nonlinear parabolic PDE systems.In this paper,for nonlinear parabolic PDE systems,using Lyapunov theory and inequality technology,the problems of mixed H₂/H_∞fault-tolerant sampled-data fuzzy control,event-triggered fault-tolerant sampled-data fuzzy control and fault-tolerant stochastic sampled-data fuzzy control are studied respectively.The specific research contents and innovations are as follows:1.A mixed H₂/H_∞fault-tolerant sampled-data control method is proposed for nonlinear space-varying parabolic PDE systems.Firstly,using T-S fuzzy model technology,a fault-tolerant sampled-data fuzzy controller is designed by constructing a Lyapunov functional that only requires to be positive definite at sampling times.Then,sufficient conditions based on spatial linear matrix inequalities（SLMIs）are obtained such that the closed-loop fuzzy PDE system is exponentially stable and satisfy the mixed H₂/H_∞performance.In order to solve SLMIs,the problem of fault-tolerant sampled-data fuzzy control for nonlinear space-varying parabolic PDE system is transformed as a linear matrix inequality（LMI）problem,and the design conditions of suboptimal mixed H₂/H_∞fault-tolerant sampled-data fuzzy controller are obtained by considering the properties of membership function.Finally,the effectiveness of the proposed control method is verified by two numerical examples.2.An event-triggered fault-tolerant sampled-data fuzzy control method is proposed for nonlinear parabolic PDE systems.Firstly,a T-S fuzzy model is given to describe the nonlinear parabolic PDE system.Secondly,considering the Markov jump failure of the actuator and spatially point measurements,an event-triggered fault-tolerant sampled-data fuzzy controller is designed.Then,the LMI-based control design conditions are obtained such that the closed-loop fuzzy PDE system is exponentially stable.Finally,a numerical example is given to verify the effectiveness of the proposed control method.3.A fault-tolerant stochastic sampled-data fuzzy control method is proposed for nonlinear delayed parabolic PDE systems.Firstly,based on the T-S fuzzy control method,considering the possibility of actuator failure,a fault-tolerant stochastic sampled-data fuzzy controller under spatially point measurements is designed.The controller considers two sampling periods whose occurrence probabilities are given constants and satisfy the Bernoulli distribution.Then,considering the properties of membership function,sufficient conditions are obtained such that the closed-loop fuzzy PDE system is mean square exponentially stable.Finally,the effectiveness of the proposed control method is verified by three numerical examples.