Preview control for uncertain discrete‐time periodic systems

Abstract

This article concerns the designing observer‐based feedback preview control and static output feedback preview control for linear uncertain discrete‐time periodic systems subject to previewable reference signal. First, a difference operator approach and a state augmentation technique are employed to derive an augmented error system. Second, considering the state unmeasured and previewable reference signal, a state observer and a preview controller are designed to achieve signal tracking performance. Then, by the Lyapunov stability theory, some sufficient conditions are obtained for the closed‐loop systems in linear matrix inequality form. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed method.

Observer-based preview control for T-S fuzzy systems

“…Because this approach is lengthy and cannot include the control performance parameters directly, under the framework of linear quadratic optimal control, optimal preview controller design methods were presented for linear time-invariant discrete-time systems (Katayama et al ., 1985; Lu et al ., 2019; Lan et al ., 2020) and linear continuous-time systems (Liao et al ., 2018; Lu et al ., 2023). Considering the requirements of actual control systems, PC has been extended to complex systems, such as uncertain systems (Li et al ., 2021a; Gershon and Shaked, 2014; Li, 2021; Xie et al ., 2023), nonlinear systems (Huang and Huang, 2020; Yu and Liao, 2019; Li and Yu, 2021), multi-agent systems (Li et al ., 2021b; Liao et al ., 2016) and large-scale systems (Liao et al. , 2018; Li and Zhang, 2021).…”

Preview controller synthesis for a class of linear parameter periodic systems

“…Subsequently, through the in‐depth research of scholars, the preview control theory has been extended to more complex systems, including descriptor systems, 16,17 nonlinear systems, 18,19 uncertain systems, 20–22 and delayed systems 23 . Certainly, as an important class of control systems, the preview control theory for periodic systems has also realized some achievements 24–27 . It should be noted that compared with the construction method of the augmented error system (AES) for periodic systems in references 24–26, the dimension of the AES in these papers is independent of the periodicity of system matrices, resulting in its reduction.…”

“…Certainly, as an important class of control systems, the preview control theory for periodic systems has also realized some achievements 24–27 . It should be noted that compared with the construction method of the augmented error system (AES) for periodic systems in references 24–26, the dimension of the AES in these papers is independent of the periodicity of system matrices, resulting in its reduction. In addition, the preview controller design in reference 27 depends on the Riccati equation and linear quadratic optimal control theory.…”