Adaptive Event-triggered Control For Uncertain Nonlinear Systems

Almost all of actual systems are nonlinear,and the linear models obtained by linearization method can only reflect the local characteristics of actual systems.On the other hand,it is usually impossible to accurately model actual systems,because of insufficient knowledge on the physical mechanism of actual system-s and its surrounding environment,inadequate accuracy of measurement tools,limitations of modeling methods and so on.This means that various uncertain-ties or disturbances inevitably exist in the obtained system models.Therefore,it is of great significance to investigate the existence and the constructive analysis and design of feedback control,according to the types/attributes of nonlineari-ties,uncertainties and disturbances.With the popularity of computer and net-work technology in control systems,it is required for feedback control to reduce the occupation of computation/communication/energy as much as possible while guaranteeing the acceptable system performance.This makes it necessary to in-vestigate more efficient feedback control,such as the event-triggered control and sampled-data control,for uncertain nonlinear systems.In this dissertation,event-triggered controls with strong feedback capability are built by combining adaptive methods for several representative classes of un-certain nonlinear systems,which can not only reduce the resource dependence,but also deal with the system nonlinearities and uncertainties/disturbances to achieve the control objectives with high accuracy and high performance.More-over,powerful schemes of adaptive output-feedback compensation are developed,which would strengthen the foundation for the exploration of event-triggered output-feedback control of uncertain nonlinear systems.Detaildedly,the main contributions of this dissertation consist of the following five parts:(I)Tracking control via adaptive event-triggered feedback for uncer-tain nonlinear systemsThe event-triggered tracking control is investigated for a class of uncertain nonlinear systems.The nonlinear systems under investigation allow large para-metric uncertainties,while the reference signal to be tracked is only currently measurable,for which no extra information is a priori known.This makes event-triggered control more challenging partially because the effect of the sampling error on the system behavior cannot be precisely bounded any more.New adap-tive event-triggered tracking schemes are proposed for the systems in two event-triggering architectures with different roles of the event-triggering mechanism on the information transmitting and control computing/updating.Specifically,a dynamic gain is incorporated in either scheme not only to compensate the seri-ous uncertainties,but also to overcome the bad influence of the sampling error.Based on the dynamic gain,two adaptive event-triggered controllers are designed with distinct event-triggering mechanisms,respectively.Particularly,to ensure application flexibility,one of the triggering mechanisms is rendered relatively in-dependent of the controller signal.The designed event-triggered controllers are shown to achieve the practical tracking for the systems,that is,the pre-specified arbitrary tracking accuracy can be guaranteed(a comparable objective to that via continuous-time control),while avoiding infinitely fast sampling/execution.(Chapter 2 in the dissertation)(II)Switching event-triggered control for uncertain nonlinear sys-temsThe event-triggered stabilization is investigated for a class of uncertain non-linear systems.Remarkably,the systems allow not only inherent nonlinearities but also the large uncertainties.The two ingredients together really challenge the control design of event-triggered stabilization,and particularly for the latter,certain compensation mechanism is necessary but hard to incorporate in the non-linear event-triggered paradigm corresponding to stabilization objective.To solve the problem,a new switching event-triggered control scheme is proposed by incor-porating a logic-based switching mechanism which has strong adaptive capability to large uncertainties.The key point of the scheme is how to flexibly couple the event-triggering mechanism and the switching varying mechanism,determining not only when to sample/execute but also when to switch the design parameter,such that the switching event-triggered controller can effectively compensate the nonlinearities,the uncertainties and the sampling error,and thus can achieve the global stabilization of the systems.Owing to the introduction of switching varying mechanism,the performance analysis of the closed-loop system is a bit complicat-ed,especially showing the nonoccurrence of infinite switchings or infinitely fast sampling/execution.Extended investigations are particularly performed for the switching event-triggered controller for its reliable implementability and broad application:By strengthening the switching varying and event-triggering mech-anisms,the modified controller can additionally guarantee the pre-evaluation of sampling/execution rate and the tolerance to more types of disturbances,respec-tively.(Chapter 3 in the dissertation)(III)Stabilizing control via more efficient switching event-triggered feedback for uncertain nonlinear systemsThe event-triggered stabilization is further investigated for uncertain nonlin-ear systems,to establish more efficient event-triggered control for the sake of reducing not only the communication load between controller and actuator but also that between sensor and controller.Specifically,more powerful and efficient switching varying mechanism and event-triggering mechanism are introduced to determine not only when to sample/execute,and when and how to switch the design parameters.Particularly,the two mechanisms can effectively not only deal with the large parametric uncertainties but especially the inherent nonlin-earities.Based on this,a switching linear(rather than nonlinear)event-triggered controller is designed to guarantee the system state to globally converge to zero,while infinite switching and infinitely fast sampling/execution are avoided.No-tably,the designed event-triggered mechanism is relatively independent of the controller signal,which makes continuous information transmitting unnecessary between sensors and controllers,while avoiding continuous control computation.(Chapter 4 in the dissertation)(IV)Dynamic feedback stabilization and disturbance rejection based on switching adaptive samplingAdaptive sampled-data stabilization and disturbance rejection are addressed,which contributes the establishment of logic-based switching adaptive sampled-data control.The disturbance concerned has a significant and persistent effect on the systems under investigation.This makes the conventional(periodic)sampled-data schemes inapplicable and forces us to employ a variable-period one with switching varying mechanism.Specifically,a switching adjustment mechanism for variable sampling periods is proposed to make sure that sampling information of the system state is rich for feedback compensation.Based on this and by in-ternal model principle,a new dynamic sampled-data controller with the variable sampling periods is proposed,which guarantees the system state to ultimate-ly converge to an arbitrary pre-specified neighborhood of the origin while the sampling periods remain unchanged after a finite number of switchings.Further-more,the dynamic control scheme is extended to establish adaptive sampled-data output regulation.(Chapter 5 in the dissertation)(V)Adaptive output-feedback stabilizing control for uncertain non-linear systemsGlobal output-feedback stabilization is investigated for two representative class-es of uncertain nonlinear systems,which contributes more powerful adaptive output-feedback compensation schemes.First,for a class of nonlinear system-s with multiple uncertainties including unknown control directions,large para-metric uncertainties and input matching uncertainty,an integrated compensa-tion mechanism via adaptive output-feedback is proposed by flexibly combining Nussbaum-gain technique,tuning function technique and extended state observ-er,based on which an output-feedback stabilizing scheme is established to achieve global convergence for the systems.Second,for a class of nonlinear systems with unknown unmeasured state dependent growth and input matching uncertainty,an adaptive output-feedback compensation mechanism with lower dynamics is proposed based on only one dynamic gain for the unknown polynomial-of-output growth rate,and an adaptive extended state observer is introduced to asymptoti-cally estimate the input matching uncertainty to render its effect well counteract-ed.Furthermore,an adaptive output-feedback controller is designed to guarantee the system state to converge to zero.(Chapter 6 in the dissertation)Based on the above research,twelve papers have been completed,where nine have been published in the famous journals or conferences on control theory(five in SCI journals),and particularly,two in "IEEE Transactions on Automatic Control" and "Automatica" which are the prestigious journals in the international control field.