Adaptive Event-Triggered Output-Feedback Stabilization For Uncertain Nonlinear Systems

Nonlinearities and uncertainties widely exist in practice,which seriously affect the feasibility and accuracy of feedback control.Effectively suppressing or eliminating their negative effects on the system is a challenging problem that needs to be studied and solved urgently.With the development of computer technology,network communication technology and control technology,networked control systems are becoming more and more popular.However,due to the limited computation and storage capacity of each component and network bandwidth,it is urgent to develop an effective strategy to reduce the need for communication/computing/storage resources as much as possible on the premise of ensuring desired system performance.In event-triggered control(ETC),sampling/execution is determined by the events on system behaviors,which not only avoids unnecessary resource consumption,but also provides timely respond to the changes of system behaviors.This endows ETC with stronger feedback capability than traditional sampled-data control.However,the discontinuity brought by the event-triggering mechanism(ETM)and the influence of sampling/execution errors would render the analysis of system performance more complicated and even lead to the degradation of system performance.In recent years,the ETC of uncertain nonlinear systems(UNSs)has become a hot topic in the field of control theory and has important theoretical significance and potential practical value.In this dissertation,powerful ETCs are developed combined with adaptive technology for UNSs,which can not only deal with the effects of system nonlinearities,uncertainties and sampling/execution error,but also reduce the sampling/execution rate.Then,the high reliable and energy-efficient control objective can be achieved,which supports the theoretical foundation for adaptive ETC of UNSs.Particularly,the funnel-based ETC strategy not only ensures the basic steady-state performance of the systems,but also ensures the prescribed convergence rate,which inspires new perspective for the prescribed performance ETC.The main contents of this dissertation include the following five aspects:(Ⅰ)Stabilizing control with time-varying threshold via adaptive eventtriggered output feedbackAdaptive event-triggered output-feedback stabilization based on time-varying threshold ETM is investigated for UNSs.Quite different from the previous works,the systems allow large uncertainties(whose size is unknown)coupled with unmeasurable states,which makes it difficult to construct the proper compensation mechanism while excluding Zeno phenomenon.To this end,adaptive event-triggered output-feedback control is established by integrating the adaptive compensation based on high gain and the time-varying threshold ETM to guarantee that the system states converge to zero while reducing the execution rate.Particularly,the threshold is strictly positive and decays to zero which is critical to avoid Zeno phenomenon and guaranteeing the desired convergence objective.(Ⅱ)Adaptive stabilization via dynamic event-triggered output feedbackThe global stabilization via adaptive dynamic event-triggered output feedback is investigated for UNSs.The differences of the approach lies in that,the ETM need to be delicately integrated with high-gain based observers,dynamic compensation for uncertainties,and the counteraction for inherent nonlinearities.Noting the potential advantages of the dynamic ETM in reducing the sampling/execution rate,a dynamic ETM is constructed by introducing a dynamic signal which is strictly positive and decays to zero.Furthermore,the dynamic event-triggered output-feedback control is designed by subtly integrating the compensation mechanism and the dynamic ETM,which guarantees the global boundedness and convergence of the system states while reducing the sampling/execution rate.(Ⅲ)Adaptive event-triggered output feedback for nonlinear systems with unknown polynomial-of-output growth rateAdaptive event-triggered output feedback for nonlinear systems with unknown polynomial-of-output growth rate is considered.Note that the time-varying threshold and dynamic threshold ETMs can only exclude Zeno phenomenon,rather than infinitely fast sampling/execution.A novel ETM is introduced to separately evaluate the behaviors of dynamic gain and controller signals.Particularly,the event on controller signal is enforced to suspend for a certain time after each execution to guarantee a positive lower bound for the inter-execution intervals.More importantly,the suspension time and threshold therein are both online adjusted according to dynamic gain,which could become adequately small as the dynamic gain increases.This ensures timely execution for the effectiveness of adaptive compensation.Then,with incorporating the ETM and the compensation of large uncertainties and inherent nonlinearities,an ETC via adaptive output feedback is proposed to make the system states converge to zero while excluding infinitely fast execution.Further attempt is performed for more efficient resource saving and disturbance tolerance.(Ⅳ)Adaptive stabilization via event-holding output feedbackThe adaptive event-holding output-feedback stabilization is investigated for UNSs.In the traditional ETMs,information transmission and control updating immediately occur once the triggering condition is satisfied.However,sometimes the systems evolve within an acceptable range although the condition holds and the control execution is not necessary at this time.Different from the traditional ETM,a time variable is introduced to record the accumulation time of events,based on which,a novel event-holding triggering mechanism is designed.The control execution occurs only when the time variable reaches the prescribed value,so that the inner execution interval can be further expanded.In addition,a dynamic high gain is introduced to compensate the large uncertainties.By subtly integrating the compensation mechanism and the event-holding triggering mechanism,the event-holding output-feedback control guarantees that the system states converge to zero,while further reducing sampling/execution rate.(Ⅴ)Adaptive event-triggered output-feedback stabilization with prescribed convergence rateAdaptive event-triggered output feedback stabilization with a prescribed convergence rate for UNSs is investigated.Different from the existing works,the systems allow completely unknown nonlinearities,from which no any information is available for feedback.To this end,a set of delicate gains,motivated by the funnel control method,are introduced not only to handle the completely unknown nonlinearities and the execution error,but also to guarantee a prescribed rate.Then,a new ETM is given,where the threshold and suspension time are online adjusted according to the gains to ensure the positive lower bound for the inter-execution intervals and the timely sampling/execution.As such,the designed event-triggered output-feedback control guarantees that the system states converge to zero with the prescribed rate.