Preview tracking control for discrete-time nonlinear Lur’e systems with sector-bounded nonlinearities

Abstract

In this paper, the problem of preview tracking control for a class of discrete-time nonlinear Lur’e systems is investigated. To overcome the difficulty arising from the sector nonlinearity, the original system is transformed into a linear parameter varying (LPV) system, and a new auxiliary method is introduced. The difference between the state vector and the auxiliary variable is used instead of the usual difference between system states. At the same time, the tracking error and the previewable future reference information are also considered in order to construct an augmented error system (AES). Then, the preview tracking problem is reduced to a robust control problem. Note that the AES is still an LPV system. Next, a state feedback controller is developed to ensure that the closed-loop system is asymptotically stable with H∞ guaranteed cost performance. Based on this, a preview controller for the original system is proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the controller.

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

“…The classical difference approach is used for system (1) to construct the augmented error system, including the tracking error and the previewable reference information. Unlike existing works, 17,21,22 the difference approach will be directly applied to the state observer (3) itself rather than the usual state equation of system (1). Here, we choose the following difference operator where η(k) is a column vector.…”

“…Since then, preview control, as an effective and appealing control technique, has received a great deal of attention and gradually formed a relatively independent theoretical framework. Up until now, the method of preview control has been widely applied to linear time-invariant systems, 12,13 linear singular systems, 14,15 linear uncertain systems, 16,17 linear stochastic systems, 18,19 some special nonlinear systems, 20,21 and so on. However, it should be pointed out that these results mentioned above are based on a common assumption that all system states are completely measurable.…”

Robust preview control for polytopic nonlinear control systems

“…Many tracking control methods are designed based on output tracking and a given reference model, that is, driving the system output to converge to the reference signal by using some control techniques (Susana Ramya et al, 2018; Tseng, 2001; Yan et al, 2019). 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.…”

Relating Lurie's problem, Hopfield's network and Alzheimer's disease

“…This problem was studied for many researchers, as Krasovskii (1953), Popov (1961), and Kalman (1963). Research on the LP also went on to other areas, such as chaos synchronization (Liao and Yu, 2008); convex approach (Gapski and Geromel, 1994); neural networks (Pinheiro and Colón, 2019); linear parameter varying (LPV) system (Yu and Liao, 2019); and µ analysis (Abtahi and Yazdi, 2019). In works like Liao and Yu (2008) and Pinheiro and Colón (2019) is shown that HNN is a particular case of Lurie type system.…”