Robust Preview Control Of Uncertain Discrete-time Systems

Preview control theory of deterministic systems has already made good progress.However,for preview control systems,some uncertainty inevitably exists.Therefore,combining the uncertain discrete-time systems theory and the preview control theory to study robust preview control of uncertain discrete-time system naturally becomes a new topic.The main research work presented in this dissertation is as follows.1.For a class of discrete-time systems with norm-bounded time-varying uncertainties,the problem of robust preview control is studied.In order to overcome the difficulty that the classical difference method in preview control theory is not applied to uncertain systems,this article finds an auxiliary method to derive an augmented error system.Then the robust controller with preview actions is obtained which guarantees the robustly stability of closed-loop system by solving a convex optimization problem.2.The preview control problem of norm-bounded uncertain discrete-time systems with time-varying delay is discussed.First,a model transformation is used to pull the time-varying delay and uncertain terms out of the time-delay system.Therefore the method of constructing the error system above can be applied to uncertain discrete-time system with time-varying delay.Then based on the scaled small gain theorem,the preview controller design method is formulated into a convex problem.Finally,numerical simulations show the effectiveness of the controller.3.The parameter-dependent preview controller design method problem is proposed for a class of polytopic uncertain discrete-time systems.The usual difference method in preview control theory can be used to uncertain discrete-time systems and then an augmented error system including previewed information is constructed,which transforms a tracking problem into a regulation problem.Then,by combining parameter-dependent Lyapunov function method with the LMI technique,the parameter-dependent preview controller is designed.4.For discrete systems with time-varying parametric uncertainties,the robust preview control is studied.First,the auxiliary variables method and the state augmentation technique are employed to derive an augmented error system with convex polyhedron structure.Then a sufficient condition based on LMI technique and the parameter-dependent Lyapunov function approach is derived for the robust asymptotic stability of uncertain systems.And the gain matrix of preview controller is obtained by solving finite linear inequalities.5.The output feedback preview control problem for uncertain discrete-time systems is studied.First,the augmented error system for uncertain discrete-time system is constructed.Then a previewable reference signal or disturbance signal is fully utilized through reformulation of the output equation for the derived augmented error system,while considering the output feedback.Finally,the static output preview controller parameter matrices can be achieved using the related theory of robust control method.The rigorous mathematical proofs for the condition of the theorems have been given in all of the case.