Optimal Preview Control for Linear Discrete‐Time Periodic Systems

Liao, Fang; Sun, Mengyuan; Usman, Usman

doi:10.1155/2019/8434293

Cited by 13 publications

(22 citation statements)

References 24 publications

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“…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.…”

Section: Construction Of the Augmented Error Systemmentioning

confidence: 99%

“…Remark 3. It is worth mentioning that Theorem 2 provides a new criterion to ensure the asymptotic stability of the closed-loop system (22) in terms of LMI. With the help of LMI toolbox in MATLAB, the observer gain L and the controller gain K can be solved simultaneously.…”

Section: Design Of the Observer-based Preview Controllermentioning

confidence: 99%

“…In this situation, using the observer-based preview controller becomes a feasible alternative solution to perform output tracking. The optimal preview control based on state observers for linear discrete-time systems was studied in Liao and Chen 22 where the observer and controller were designed separately with the aid of the separation principle. Unfortunately, as for nonlinear systems, the nonseparation of the observer and controller gains inevitably leads to bilinear matrix inequality (BMI) formulations in design conditions, which brings some difficulties in computation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Liao

2014

Advances in Mechanical Engineering

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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.

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Section: Construction Of the Augmented Error Systemmentioning

confidence: 99%

Section: Design Of the Observer-based Preview Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Liao

2014

Advances in Mechanical Engineering

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“…This paper investigates linear discrete-time periodic systems and presents a new design method of optimal preview controller for such a system. Compared with Liao et al (2019), the system in this paper is more general, in which state matrix, input matrix and output matrix are periodic. First, using the lifting procedure in Liao et al (2019), the original system is converted into a time-invariant system.…”

Section: Introductionmentioning

confidence: 99%

Design of an optimal preview controller for linear discrete-time periodic systems

Sun

Liao

Deng

2021

Transactions of the Institute of Measurement and Control

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In this paper, the preview tracking control problem for linear discrete-time periodic systems is considered. First, to overcome the difficulty arising from periodicity of the system, the linear discrete-time periodic system is transformed into an ordinary time-invariant system by lifting method. Secondly, the difference between a system state and its steady-state value is used to derive an augmented system instead of the usual difference between system states. Then, the preview controller for the augmented system is proposed by the preview control theory, which solves the preview tracking control problem for the periodic systems. Moreover, an integrator is introduced to ensure that the output can track the reference signal without static error. Finally, the obtained results are illustrated by the simulation examples.

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“…In order to guarantee the robustness for the unknown disturbance in the sense of L 2 gain, the H ∞ criterion has been introduced into the PC problems 21‐23 . Moreover, under the assumption that the reference signal is previewable, 24‐27 considered the robust PC problem based on LMI technique and the augmented error approach. Meanwhile, the application of PC theory has also made great progress.…”

Section: Introductionmentioning

confidence: 99%

Observer‐based preview repetitive control for uncertain discrete‐time systems

2020

Intl J Robust & Nonlinear

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In this paper, the preview repetitive control (PRC) problem is considered for uncertain discrete‐time systems subject to a previewable periodic reference signal. First, an augmented system including future information on the previewable reference signal is constructed. Second, considering the state unmeasured and periodic tracking reference signal, state observer and preview repetitive controller (PRCr) are designed in both state feedback and output feedback settings. To achieve signal tracking performance, a two‐dimensional (2D) model approach and some LMI technique are presented to describe the control and learning actions of the PRC system by using the lifting technique. Then, by Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of LMIs, and meanwhile, the design of a repetitive controller with preview actions is proposed through the LMI approach. Finally, two examples illustrate the effectiveness of the results.

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Optimal Preview Control for Linear Discrete‐Time Periodic Systems

Cited by 13 publications

References 24 publications

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

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

Design of an optimal preview controller for linear discrete-time periodic systems

Observer‐based preview repetitive control for uncertain discrete‐time systems

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