Robust Event-Triggered Control For Piecewise Affine Systems

As an important branch of hybrid system,piecewise affine system consists of finite number of affine subsystems and the corresponding operating region of each subsystem.Nonlinear systems can be approximated by piecewise affine systems with arbitrary ac-curacy,which makes piecewise affine system a powerful tool to analyze and synthesize nonlinear systems.And therefore,piecewise affine system has a wide scope of engineer-ing applications.There are much work about stability analysis and controller design of piecewise affine systems,however,few literature on event-triggered control design for piecewise affine systems.Different from traditional time-triggered control mechanism,event-triggered control is an aperiodic control scheme where control tasks are executed on-demand.Compared with the traditional periodic control,event-triggering approach has the advantages of saving network,computing and energy resources.Therefore,it is of great theoretical and practical significance to study the event-triggered control of the piecewise affine systems with considering its robustness.Thus,this thesis studies the following aspects for different control situations:1.The problem of event-triggered control is studied for piecewise affine systems with parameter uncertainties.Different event-triggering schemes are proposed to design the event-triggering controller.The control performance of the system is considered and the quadratic performance index of the system is designed.By combining the piecewise Lyapunov function,the controller design problem is transformed into the optimization problem in the form of linear matrix inequalities.By adjusting the weighting matrix of the cost function and the event-triggered parameters,the unique optimal controller can be obtained.Numerical simulations are given to show the feasibility and effectiveness of the proposed methods.2.Event-triggered H_?control is investigated for piecewise affine systems in the context of external disturbance.With the aid of piecewise Lyapunov function and some convex tools,the problem of event-triggered H?controller design is transformed into a stability condition described by linear matrix inequalities.The controller can be derived by solving a series of linear matrix inequalities.Some simulation examples are provided to show the feasibility and effectiveness of the proposed approaches.3.The synthesis problem of the event-triggered H?controller for piecewise affine system with control input saturation is proposed.Two methods,namely the sector method and the auxiliary matrix method are utilized to deal with the controller saturation respec-tively.In order to further save communication resources,an event-triggered strategy considering saturation information is proposed.Based on the piecewise Lyapunov technique,the condition based on linear matrix inequality is derived,which not only guarantees the stability of the closed-loop system under certain performance index of H?,but also re-duces the number of transmission signals.Numerical examples are provided to verify the effectiveness and superiority of the proposed methods.4.For discrete-time piecewise affine systems with parameter uncertainties,a novel event-triggering scheme is proposed and an observer based output feedback controller is designed.Based on the ellipsoid description of the operating regions and the piecewise Lyapunov function,the co-design problem of observer,controller and event-triggering strategy is transformed into a stability condition described by linear matrix inequalities,which ensures the stability of the closed-loop system.Some numerical examples are given to show the feasibility and effectiveness of the proposed approaches.