Design Of Event-triggering Mechanisms For Nonlinear Control Systems

Event-triggered control(ETC),a new control strategy in which the control task is executed after the occurrence of a fixed event,is different from conventional periodic control in which the control task is executed after the elapse of a fixed periodic time.The core of design of a typical event-triggering mechanism(ETM)is to guarantee the stability and performance of the closed-loop system,that is to say,the transmission of the outputs or states of the plant and updates of the controller only take place when needed from a stability and performance point of view,consequently reducing utilization of the limited resources.Although the potential application of ETC is fantastic,little theoretical results have been made based on strict mathematic concepts.The main reason is that the system behavior of ETC systems(ETCSs)is hybrid,it contains both continuous and discrete behaviors,which makes the system analysis difficult.Even so,the re-cent developments of hybrid system theorem provide opportunities and challenges for enriching theoretical results in the field of ETCSs.Based on the existing results,this thesis investigates ETC for nonlinear systems,and the main contributions are outlined as follows:Based on Lyapunov functions,the problem of ETC for a class of nonlinear systems is in-vestigated.By enforcing that the Lyapunov function is bounded by a constructed asymptotically convergent function along the trajectory of the closed-loop system,a Lyapunov-based ETM is proposed for a class of nonlinear systems.It is proved that the trajectories of the closed-loop system with static,dynamic and Lyapunov-based ETMs have the same guaranteed decay rate,and also for any given state of the system,the next execution time given by the Lyapunov-based ETM is larger that these given by static and dynamic ETMs.Based on dwell time,the problem of ETC is addressed for a class of nonlinear systems.Un-der some mild conditions,by using the predictability of the bound of certain values of the states of nonlinear control systems,two efficient and constructive ways are given to find suitable dwell times for static and dynamic ETC.One method is based on sufficient Lyapunov-like conditions on stabilization of nonlinear systems,and the other one is from applying Barbalat's lemma.Then both static and dynamic ETC strategy with dwell times for a class of nonlinear state-feedback systems are presented.The problem of ETC and self-triggered control(STC)is studied for a class of nonlinear sys-tems without input-to-state stable(ISS)limit.By using perturbation theories and Taylor's the-orem,new event-triggering and self-triggering mechanisms are presented for nonlinear control systems which are not necessarily ISS with respect to measurement errors.Both two mechanism-s can guarantee the uniform ultimate boundedness of the solutions of the resulting closed-loop systems and the existence of a positive lower bound for inter-execution times.Based on threshold signal,the problem of ETC for a class of nonlinear systems is investigat-ed.By modeling the sampled-data state-feedback control system as a perturbation of nominal continuous state-feedback control system and using perturbation theories,a new ETM is pro-posed for a class of nonlinear systems with an exponentially converging threshold signal.It is proved that the presented ETM guarantees not only the exponential convergence of the solution of the ETCS but also the existence of a positive lower bound for inter-execution times.The problem of sampled-data control is studied for a class of stochastic control systems.Based on variant sufficient conditions on stabilization of stochastic nonlinear system,the prob-lem of computing the maximal allowable sampling period(MASP)is transformed into solving transcendental equations.The solution of the transcendental equation gives an upper bound on MASP guaranteeing asymptotic stability or exponential stability of the sampled-data control sys-tem in mean square.By using the estimated bound on MASP,a ETM with dwell time is proposed for a class of stochastic control systems.