Robust Event-Triggered Control Of Nonlinear Systems With A Rule-based Triggering Mechanism

Time-triggered sampling and event-triggered sampling are two different sampling meth-ods for signals that are defined on continuous time-line.Control based on periodically time-triggered sampling is the basis for the traditional computer control.Different from period-ically time-triggered control,the basic idea of event-triggered control is to determine when the control actions should be applied according to the online state of the control system.Event-triggered control has been recognized to be useful in further reducing the computation and communication resources.Furthermore,for many nonlinear systems,periodic sampling can only guarantee semi-global stabilization,while event-triggered sampling may achieve global stabilization.Due to the reasons above,event-triggered control has been one of the hottest research topics in control theory community.Disturbances and uncertainties are ubiquitous in the world.In the presence of distur-bances and uncertainties,the basic triggering mechanism can lead to the phenomenon of infinitely fast sampling.Theoretically,this destroys the forward completeness of the system.Practically,this causes waste of computation and communication resources.Also,nonlin-ear systems are often quite sensitive to disturbances and uncertainties.For example,even a disturbance that is small and converging to zero in finite time may lead to divergence of a system that is globally asymptotically stable when the disturbance is zero.Thus,robust event-triggered control of nonlinear systems has been recognized to be one of the fundamen-tal problem in the field.So far,there are mainly three methods that are used to deal with disturbances and uncertainties:?-modification,event-time mixed triggering,and dynamic event triggering.Although the designs based on e-modification are able to avoid infinitely fast samplling,but the price paid for this is the loss of asymptotic convergence.The approach of event-time mixed triggering introduces time-triggering to avoid infinitely fast sampling,but the time triggering mechanism is the primary when the system is subject to disturbances,which means that the system is more like a periodically time-triggered system.The known dynamic event-triggered control results mainly focus on the disturbances and uncertainties that do not change the system equilibrium.Based on the previously known results,this work proposes a new,rule-based event-triggering mechanism to solve the robust event-triggered control problem for nonlinear sys-tems subject to disturbances and uncertainties.The thesis mainly includes the following three aspectsFirst the thesis considers a class of nonlinear systems subject to external disturbances,and proposes a rule-based event-triggering mechanism.If the plant admits a control law that is robust with respect to measurement errors,then the combination of the control law and the event-triggering mechanism results in a robust event-triggered control law,which is able avoid infinitely fast sampling and at the same time guarantee the gain property from the external disturbance to the state error.If moreover,the external disturbance converges to zero,then the state error converges to the origin.The robustness and gain properties are described by input-to-state stability.By extending the robust event-triggered state-feedback control result to systems with dynamic uncertainties,the thesis proposes a result on robust event-triggered control for non-linear systems with dynamic uncertainties.The basic idea is to transform the closed-loop system into an interconnection of input-to-state stable subsystems,and to employ the nonlin-ear small-gain theorem to guarantee the robust stability of the closed-loop system.Based on the proposed robust event trigger designs,the thesis considers a class of un-certain nonlinear systems,and designed nonlinear observers and controllers,such that the closed-loop system can be transformed into the form that is studied in Chapter 4,and the robust event-triggered output-feedback control problem is solved accordingly.