| Parabolic systems are characterized by spatio-temporal variation.The system variables not only vary continuously in time,but also are widely distributed in space.It has been widely used in reaction diffusion problems,such as modeling and control of infectious diseases,chemical reaction control,heat conduction control and pipeline flow control.The stabilization and tracking of systems are two typical problems in control theory,and the stability and stabilization of systems are the basis for studying other properties of systems.In addition,the tracking control problem is a kind of basic control problem in engineering practice,such as the tracking control problem of temperature in the heat conduction process,the tracking control problem of spinning solution concentration in the fiber forming process,and the tracking control problem of biological enzyme diffusion rate.Therefore,the research on stabilization and tracking control of parabolic systems has important theoretical significance and practical application value.Some important results have been obtained on the control of semilinear parabolic systems,such as approximating corresponding semilinear parabolic systems on bound-ed closed sets based on the Takagi-Sugeno fuzzy model or fuzzy logic system/neural network approximation theory,and obtaining local stability results.However,there are few reports on the researches of global control methods for semilinear parabolic systems.In addition,in the actual engineering system modeling,on the one hand,considering the insufficient accuracy of measurement tools,unclear understanding of the working mechanism of the controlled object and the limitations of cost and exist-ing technology,it is difficult to identify the controlled system from time to time,so that it is difficult to obtain the accurate mathematical modeling of the system.On the other hand,the complex external environment brings many uncertain influences to the controlled system.However,the existence of these uncertainties may pose a great threat to the stability of the system.Therefore,the stabilization and tracking control of semilinear parabolic systems with different uncertainty characteristics(such as uncertain external interference,unmodeled dynamic uncertainty and uncertainty coefficient)will be studied in this dissertation,and a series of solutions to these prob-lems are proposed to further enrich the researches in this direction.Specific research contents include the following aspects:1.For semilinear parabolic systems with uncertain nonlinear function and uncertain external disturbance,a robust piecewise adaptive control method is designed to achieve global asymptotic stability of the closed-loop systems in the sense of L~2 norm.Then,by constructing an appropriate Lyapunov functional and using the Wiritinger’s inequality and a variant of the Agmon’s inequality,it is shown that the proposed robust piecewise adaptive controller not only ensures the globally L~2 asymptotic stability of the closed-loop systems,but also satisfy the given disturbance attenuation performance.2.For uncertain semilinear parabolic systems with spatiotemporal faults,an integrat-ed scheme of spatiotemporal fault detection and control consisting of a fault detection observer,a fault estimator and a feedback controller based on the fault estimator is de-signed,which makes the coupled systems globally uniformly ultimately bounded.This strategy mainly includes the following three steps.Firstly,a fault detection observer is constructed by using average measurement,and the deviation signal generated by the observer is used to detect the existence of the fault.Secondly,a fault estimator with a fault estimation algorithm is designed,which starts to perform only when the fault observer detects the existence of a fault.Thirdly,a feedback controller based on fault estimator is designed to make the coupled systems globally uniformly ultimate-ly bounded.Sufficient conditions are derived to ensure the coupled systems globally uniformly ultimately bounded by using the Lyapunov stability theory.3.For parabolic systems with periodic time-varying nonlinear parameters,an adaptive neural network controller is designed to make the systems globally L~2 asymptotically stable.Firstly,an uncertain nonlinear dynamical system is presented by using neural network and Fourier series expansion.Secondly,based on the adaptive fuzzy control technique and the reparameterization method,two controller are designed to make the parabolic systems with nonlinear periodic time-varying parameter asymptotically L~2 stable,and the sufficient conditions for the L~2 asymptotical stability of the closed-loop systems are derived.In addition,this method can be extended to the control problem of parabolic systems with time delays,external disturbances and nonlinear periodic time-varying parameter.Two robust adaptive neural network control algorithms are designed to make the parabolic systems asymptotically L~2 stable and meet the given disturbance attenuation performance.4.A piecewise adaptive fuzzy control algorithm is designed for a semilinear parabolic systems with uncertain external disturbances and unmodeled dynamic uncertainties based on the approximate theory of fuzzy logic systems and adaptive bounded tech-nology,which makes the systems track the target systems globally.Based on operator semigroup theory,the existence and uniqueness of system solutions are analyzed.Then,a new global adaptive fuzzy controller is designed to solve the global L~2 asymptotic tracking control problem of a class of semilinear parabolic systems with uncertainty coefficients besides the two uncertainties mentioned above.In addition,the global asymptotic tracking condition is obtained,which overcomes the semi-global tracking control results.5.An adaptive event triggered tracking controller is designed for semilinear parabolic systems with time-varying delay,which enables the systems to track the target sys-tems asymptotically and reduce resource consumption.Firstly,Takagi-Sugeno fuzzy models are introduced to describe the semilinear parabolic systems.Secondly,a less conservative and more general fuzzy dynamic event-triggered strategy is proposed to reduce communication consumption and avoid unnecessary continuous signal monitor-ing.Since the dynamic threshold is closely related to the currently sampled signal and the latest successfully transmitted signal,it can be promptly dynamically adjusted.In addition,on the basis of a reasonable assumption,a novel linear matrix inequality relax technique is introduced to deal with the mismatched premise variables between the fuzzy systems and the fuzzy controller.By constructing the appropriate Lyapunov-Krasovskii candidate functional,the criteria that the semilinear parabolic systems can asymptotically track the target systems is derived,and the desired dynamic event-triggered controller gains can be obtained by solving a set of linear matrix inequalities.The proposed dynamic event-triggered strategy reduces effectively communication re-source consumption. |
