Adaptive Boundary Control For Several Classes Of Uncertain Partial Differetial Equation Systems

Partial differential equation(PDE)systems are often used to describe practical dynamic processes with spatial and temporal-varying features,and ordinary differential equation(ODE)systems can only partly describe the characteristics of these dynamic processes.On the other hand,uncertainties inevitable exist in the systems,due to the incomplete knowledge on the physical mechanisms of the controlled plants and surrounding environment,the limitation of the modeling methods,the inadequate accuracy of measurement tools and so on.Moreover,different from the in-domain control requiring actuators to be set in the interior of systems,boundary control requires actuators to be imposed only on the boundary of systems,and thus has the advantages of non-intrusion,easy implementation and low cost.Therefore,it is of great significance to study the boundary feedback control of uncertain PDE systems.In this dissertation,for several classes of uncertain PDE systems,suitable compensation mechanisms for parametric uncertainties are introduced by adaptive technique,and then novel boundary feedback control strategies are developed by combining infinite-dimensional backstepping method to guarantee the convergence of system states.In addition,to save communication and/or computation resources,by integrating adaptive compensation mechanisms with eventtriggering mechanisms,effective event-triggered feedback strategies are proposed to ensure the stability of closed-loop systems,while excluding Zeno phenomenon.The main works of this dissertation consist of the following five aspects:(?)Adaptive feedback stabilization for uncertain first-order hyperbolic PDE-ODE cascade systemsBoundary stabilization for a class of uncertain first-order hyperbolic PDE-ODE cascade systems is addressed.Different from the related literature,unknown spatial-varying and unknown constant parameters are allowed in the PDE and ODE subsystems,respectively.This brings technical challenges into the analysis and synthesis of boundary control,especially requires powerful compensation mechanism to be introduced for the multiple parametric uncertainties.For this,under an infinite-dimensional backstepping transformation and its inverse,the original system is first transformed into a nw system(called target system),which facilitates the control design and performance analysis.Then,by incorporating the adaptive technique based on projection operator,a novel compensation strategy is proposed for unknown parameters.Finally,a desired boundary controller is designed to guarantee that the states of the original system converge to zero in the sense of L2-norm.(Chapter 2 in the dissertation)(?)Adaptive output-feedback stabilization for PDE-ODE cascade systems with unknown control coefficient and spatial-varying parameterOutput-feedback stabilization for a class of uncertain first-order hyperbolic PDE-ODE cascade systems is investigated.The PDE subsystem under investigation allows both unknown control coefficient and unknown spatial-varying parameter,and only one boundary value of the PDE subsystem is measurable.The parametric uncertainties coupling to the unmeasured states make the control problem more challenging.For this,an invertible transformation is first introduced to combine the two unknown parameters into one,and meanwhile to change the system into an observer canonical form,based on which a couple of filters are constructed to rebuild the unmeasurable states.Finally,by adaptive technique and infinite-dimensional backstepping method,a boundary feedback controller is designed to guarantee that all the signals of the resulting closed-loop system are bounded,while the original system states converge to zero.(Chapter 3 in the dissertation)(?)Adaptive stabilization via event-triggered feedback for uncertain hyperbolic PDE-ODE cascade systemsWith the population of networked control systems,a series of problems such as the overloaded burden of network bandwidth and the shortage of node energy have become increasingly sharp,and it is necessary to realize the efficient utilization of communication and/or computation resources,under the premise that the system stability is guaranteed.In view of the outstanding advantage of event-triggered control in saving communication and/or computation resources,the event-triggered boundary stabilization for a class of first-order hyperbolic PDE-ODE cascade systems with multiple unknown parameters is addressed.Different from the related works,in which the system parameters are all required to be precisely known,the system under investigation allows unknown parameters.For this,it is important to build suitable compensation mechanism for the parametric uncertainties,and to integrate the compensation mechanism with event-triggering mechanism to ensure the desired system performance.Specifically,by incorporating infinite-dimensional backstepping method and adaptive technique,a compensation strategy for parametric uncertainties is first developed,and meanwhile a dynamic event-triggering mechanism is constructed to determine the execution times.Finally,a desired feedback controller is explicitly designed to guarantee that all the signals in the closed-loop system are bounded and the original system states converge to zero in the sense of L2-norm,while ensuring a positive lower bound for th e inter-execution intervals.(Chapter 4 in the dissertation)(?)Adaptive stabilization via event-triggered output-feedback for uncertain first-order hyperbolic PDE systemsEvent-triggered output-feedback stabilization is investigated for a class of uncertain first-order hyperbolic PDE systems.Remarkably,the system under investigation allows multiple unknown parameters and only one measurable boundary value.This renders the control design and performance analysis more challenging,especially how to design appropriate compensation mechanism and unmeasurable states reconstruction mechanism,and integrate these mechanisms with the event-triggering mechanism.By introducing a couple of filters,the unmeasurable states are first rebuilt.Based on this,by flexibly integrating infinitedimensional backstepping method and time-varying threshold strategy,a novel adaptive event-triggered output-feedback controller is successfully designed.Particularly,by introducing a time-varying signal into the threshold,which decays to zero as time goes infinity,an event-triggering mechanism is constructed to determine execution times.It is shown that the designed feedback controller can guarantee that all the signals of the resulting closed-loop system are bounded and Zeno phenomenon can not happen,and furthermore ensure that the state of original system converges to zero.(Chapter 5 in the dissertation)(?)Exponential stabilization via event-triggered output-feedback for 2×2 hyperbolic systemsBoundary stabilization via event-triggered output-feedback for a class of 2×2 hyperbolic systems with spatial-varying parameters is addressed.The considered system only requires that one boundary value is measurable.Then,compared with the closely related works,the system needs less information to be available for feedback.This enlarges the application scope of the proposed control method.By the measurable information,an observer is constructed to estimate the unmeasurable states by infinite-dimensional backstepping method.Then,by incorporating the time-varying threshold strategy,a novel event-triggered outputfeedback controller is designed for the system.Particularly,controller signal and a time-varying signal decaying to zero as time goes infinity are introduced into the threshold to enlarge the inter-execution intervals.It is shown that the designed feedback controller can guarantee that no Zeno phenomenon occurs,and furthermore all the signals of the resulting closed-loop system exponentially converge to zero in the sense of L2-norm.(Chapter 6 in the dissertation)...