Event-Triggered Control For Piecewise-Affine Systems

The piecewise-affine system is mainly defined by a finite number of subsystems and the corresponding convex polyhedron domains.The piecewise-affine system can approximate the nonlinear system with arbitrary accuracy,which is determined by the number of domains.Therefore,the piecewise-affine system is considered to be a powerful tool for researching nonlinear systems and has a wide range of applications.There are many existing results on stability analysis and controller design of piecewise-affine systems.On the other hand,event-triggered control has received much attention in recent years due to the advantages of less resource utilization compared to the traditional control strategy.In recent years,event-triggered control has been applied to many systems.However,the study of event-triggered control for piecewise-affine system has not been proposed.Therefore,this thesis mainly studies the controller design of piecewise-affine system under event-triggering scheme in different situations.The research work of this thesis can be divided into the following aspects.For the problem of controller design under event-triggering scheme in piecewise-affine system,event-triggering condition and event-triggering state feedback controller are designed.Firstly,based on Lyapunov stability theory,sufficient condition is given to guarantee the asymptotic stability of the system in the form of linear matrix inequality(LMI).Secondly,by taking the control performance into consideration,the quadratic cost function is given.The control performance is optimized by minimizing the upper bound of the quadratic cost function.The optimal controller gain under event-triggering scheme is obtained by solving LMI.Finally,simulation examples are given to demonstrate the effectiveness and advantages of the proposed approach,where the number of control input updates is reduced,while the control performance is still guaranteed.The problem of event-triggered control is investigated for discrete-time piecewiseaffine systems subject to input saturation.Firstly,by introducing the nonlinear dead-zone function to represent the saturation characteristic in order to form a LMI based on local stabilization criteria.Then,unique state-feedback control gain can be obtained by solving the LMI problem under the event-triggering strategy.The local asymptotic stability of the system is guaranteed.The domain of attraction is estimated and maximized with the controller synthesis via ellipsoidal approximations.Finally,simulation examples are given to show that the proposed approach can deal with input saturation effectively.To solve the problem of event-triggered control for piecewise-affine system with input saturation and bounded disturbance,a convex hull method is proposed.Firstly,the auxiliary feedback matrix is introduced to deal with the problem of input saturation.Sufficient condition for guaranteeing local asymptotic stability of the system is proposed in the form of LMI and the event-triggered controller is obtained and the domain of attraction is estimated.Meanwhile,an optimization problem for maximizing the domain of attraction is formulated in LMIs.Then,for input-saturated piecewise-affine systems with bounded disturbance,event-triggered anti-disturbance controller based on state feedback is designed to ensure that the system is ultimate uniformly bounded(UUB).The simulation examples are given to show that the designed controller can effectively deal with the input saturation,reduce the influence of disturbance while reducing the number of data transmission.