Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

Abstract

<jats:p> In this article, the observer-based preview tracking control problem is investigated for a class of discrete-time Lipschitz nonlinear systems. To convert the observer-based trajectory tracking problem into a regulation problem, the classical difference technique is used to construct an augmented error system containing tracking error signal and previewable reference knowledge. Then, a state feedback controller with specific structures is taken into consideration. Sufficient design condition is established, based on the Lyapunov function approach, to guarantee the asymptotic stability of the closed-loop system. By means of some special mathematical derivations, the bilinear matrix inequality condition is successfully transformed into a tractable linear matrix inequality. Meanwhile, the gains of both observer and tracking controller can be computed simultaneously only in one step. As for the original system, the developed tracking control law is composed of an integrator, an observer-based state feedback controller, and a preview action term related to the reference signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical method. </jats:p>

Robust preview control for polytopic nonlinear control systems

“…A non-link rigid robot (O-LRR) under gravitation field is cited in Yu and Liao (2020). The continuous-time state-space model of the O-LRR control system is described as…”

“…When the future information of the reference signals was available, Yu and Liao (2019) and Yu et al (2018) investigated the problem of preview tracking control for a class of nonlinear systems. More recently, the observer-based preview tracking control is investigated for discrete-time Lipschitz nonlinear systems (Yu and Liao, 2020).…”

“…Compared with the existing studies (Lan et al, 2019; Li and Liao, 2017; Takaba 2000; Yu and Liao, 2019; Yu and Liao, 2020; Yu et al, 2018), the proposed design method can cope with linear discrete-time system models subjected to nonlinear term and polytopic uncertainites, which can provide a wider application scope. The key contribution of this paper can be summarized as below: (1) An augmented error system including previewed information is constructed.…”

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

“…Subsequently, linear matrix inequality (LMI) technique has been extensively used to handle the PC problems for uncertain discrete-time systems [6]. Combining LMI-based PC with other control schemes, some new concepts are proposed, such as adaptive PC [7], fault tolerant PC [8], H ∞ PC [9], observer-based PC [10], and distributed PC [11]. However, in continuous-time systems, the methods that can be used to deal with PC issue are relatively limited, and differential operation is widely used instead of differential operation [12][13][14][15][16].…”

“…Remark 2. Different from (2), there is no time delay in the state space model of the RC system represented by (10), so an augmented error system without time delay can be obtained.…”