Abstract
This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.
Highlights
Preview control is an important control technique for improving the tracking performance of the closed-loop system by utilizing the known future information about reference signals or disturbances [1,2,3]
This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems
In [5,6,7], the robust preview control schemes were established to realize the problem of asymptotic output tracking for several types of uncertain linear discrete-time systems
Summary
Preview control is an important control technique for improving the tracking performance of the closed-loop system by utilizing the known future information about reference signals or disturbances [1,2,3]. In [4], the information fusion estimation technique was adopted to address the discrete linear preview tracking problem. In [5,6,7], the robust preview control schemes were established to realize the problem of asymptotic output tracking for several types of uncertain linear discrete-time systems. In [8, 9], the design of optimal preview controller for continuous- and discrete-time linear descriptor systems was developed via the classical difference method. In [10], the stochastic linear quadratic optimal tracking problem with preview compensation for linear continuous-time Markovian jump systems was investigated. In addition to the theoretical progresses, practical applications can be found in many realistic physical systems such as vehicle suspension systems [11, 12], robot systems [13], and rigid body motion control systems [14, 15]
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