Preview Control For Several Classes Of Nonlinear Systems

Preview control is an important control technique to enhance the tracking performance of the closed-loop system by utilizing the future information of the reference signals or disturbances,and it has been successfully applied to many practical problems.Nonlinear phenomena widely exist in the fields of nature and engineering technology.Thus,the study of nonlinear systems has attracted considerable attention of scholars at home and abroad.According to the basic idea of preview control,this paper studies the output tracking problem for several classes of nonlinear systems.The specific research contents of this paper include the following aspects:1.For a class of differentiable Lipschitz nonlinear systems,the error system method is adopted to study the preview tracking control problem and obtain an ideal control scheme.The use of the differential mean value theorem helps to overcome the difficulty of dealing with the difference of the nonlinear terms and also guarantee that the augmented error system has a structure similar to linear parameter varying system.Furthermore,a suitable state feedback controller is proposed by applying the existing result.By returning the controller back to the original system,a concrete form of the tracking controller with preview action is presented.2.The design of preview tracking controller for a class of differentiable Lipschitz nonlinear time-delay systems is considered.By introducing the backward difference operator,the original system is transformed into a discrete-time uncertain time-delay system in form.Then,taking the tracking error and the previewable information of the reference signal into account,an augmented error system with time-delay is derived.By applying Lyapunov stability theory and LMI technique,the design of a memory state feedback controller is presented in the form of LMI.Based on this,the preview controller for the original system is obtained.3.The preview control problem of a class of differentiable Lipschitz nonlinear systems with norm-bounded uncertainties is dealt with.An augmented error system is constructed by means of a simplified auxiliary method.The introduction of discrete integrator has the capability of eliminating the static error of the system.By solving a linear matrix inequality problem,a state feedback controller is designed under which the closed-loop system is asymptotically stable with H? performance.Returning the controller back to the original system,the preview control scheme is obtained.4.For a class of more general Lipschitz nonlinear systems,the problem of tracking control with preview is addressed via state feedback and output feedback.By utilizing the backward difference technique,the augmented error system with formally nonlinear characteristics is constructed.The tracking problem is reduced into a stabilization problem.Then,both state feedback control and static output feedback control are considered.Based on Lyapunov stability theory,the sufficient condition for asymptotic stability of the closed-loop system is proposed.According to this stability criterion,the preview controller design for the original system is obtained.This result is also applicable to Lipschitz system where the nonlinearity is not differentiable.5.For a class of nonlinear Lur'e systems with sector-bounded nonlinearities,the tracking control method with preview action is discussed.In order to overcome the difficulty arising from sector-bounded nonlinearity,the system is reformulated by a formal linear parameter varying system.A novel auxiliary approach is adopted to derive the augmented error system that includes the known future information of the reference signal and the tracking error.The tracking problem with preview action is thus transformed into a robust control problem.Then,a suitable state feedback controller is designed to ensure that the closed-loop system is asymptotically stable and satisfies H?.guaranteed cost control performance index.Based on this,the preview controller for the original system is obtained.All the conclusions in this paper have been proved by strict mathematical derivation,and the effectiveness of the proposed preview controller has been verified by numerical simulations.