Design of an Optimal Preview Controller for Continuous-Time Systems

Liao, Fang; Tang, Yuan Yan; Li, Heping; Wang, Yunjian

doi:10.1142/s0219691311004250

Cited by 40 publications

(64 citation statements)

References 4 publications

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“…The conclusion comes from Theorem 4.1-4.3 and Katayama et al (1987); Liao et al (2011);Liao et al (2016);Zheng (2002).…”

Section: Global Optimal Preview Controller Of the Original Systemmentioning

confidence: 85%

“…Compared with Katayama et al (1987); Liao et al (2011);Liao et al (2016), we further develop the theory of the preview control, and successfully apply it to the cooperative tracking problem. Furthermore, since the regulated output is taken as a component of the augmented state vector, the certain matrix equations, which are required in distributed output regulation problems (see, e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Next, the optimal control inputu(t ) will be determined that can minimiseJ under system (21). By employing the results of Katayama et al (1987); Liao et al (2011);Liao et al (2016), the following theorem can immediately hold.…”

Section: Optimal Controller Of the Augmented Systemmentioning

confidence: 95%

“…As stated in Athans (1971;Katayama et al (1987);Liao et al (2011);Liao et al (2016), by introducing the derivative of u(t ) into J, the integral of e(t ) will be incorporated in an optimal controller, which has the property of eliminating the static errors.…”

Section: Remark 32mentioning

confidence: 99%

“…In Katayama and Hirono (1987); Katayama, Ohki, Inoue, and Kato (1985), the preview tracking problem was considered in discrete-time and continuous-time settings, respectively, and type-one servo controllers were derived by applying state augmentation technique and linear quadratic integral technique. Based on the results of Katayama et al (1987), Liao, Tang, Liu, and Wang (2011) investigated the scenario that the reference signal and external disturbance were previewable simultaneously. In recent years, a number of significant results about the preview theory were produced by combing with other control issues.…”

Section: Introductionmentioning

confidence: 99%

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Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

Liao

Deng

et al. 2017

International Journal of Systems Science

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This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

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“…The conclusion comes from Theorem 4.1-4.3 and Katayama et al (1987); Liao et al (2011);Liao et al (2016);Zheng (2002).…”

Section: Global Optimal Preview Controller Of the Original Systemmentioning

confidence: 85%

Section: Discussionmentioning

confidence: 99%

Section: Optimal Controller Of the Augmented Systemmentioning

confidence: 95%

Section: Remark 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

Liao

Deng

et al. 2017

International Journal of Systems Science

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H_∞optimal preview tracking control problem with disturbance attenuation

Liu

2022

Asian Journal of Control

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In this paper, the H∞ optimal preview tracking control problem of continuous‐time linear system with external disturbance is studied, where the reference signal is previewed and its amplitude does not decay. First, an augmented system with error vector, original system state derivative, and internal model state derivative is constructed, which transforms the tracking problem into the H∞ optimal output regulation problem. Second, the H∞ optimal control method is used to design the controller, and the output regulation of the augmented system is achieved by finding the upper bound of the discount factor. Then the optimal controller, including error integral, preview feed‐forward compensation, and internal model compensation, is obtained for the original problem, and meanwhile the sufficient conditions are also provided to guarantee the existence of the controller. Finally, both theoretical and simulation results show that under the proposed controller, the closed‐loop system can achieve asymptotic tracking and has robustness against the disturbance.

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Design of zero‐sum game‐based H∞$$ {H}_{\infty } $$ optimal preview repetitive control systems with external disturbance and input delay

Liu,

Lan

2024

Intl J Robust & Nonlinear

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In this article, an optimal preview repetitive control (OPRC) scheme is proposed to deal with the disturbance attenuation problem for continuous‐time linear systems with external unknown disturbance and input delay. A general bounded gain is applied to the OPRC tracking control problem by introducing a function with discounted performance. First, an augmented system containing system state equation, tracking error dynamics, and modified repetitive control output equation is constructed, which is then transformed into a non‐delayed one by state transformation. Next, the OPRC controller is given and the game algebraic Riccati equation (GARE) is derived by transforming the tracking problem into a 2‐player zero‐sum game problem to give a Nash equilibrium solution of the associated min–max optimization problem. Besides, a value iteration (VI) algorithm is introduced to optimize the solution of continuous time GARE and ensure its convergence. Furthermore, the bounded‐input bounded‐output stability of the closed‐loop system is obtained by giving an upper bound on the discount factor. Finally, the numerical simulation example is provided to illustrate the effectiveness of the proposed method.

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Design of an Optimal Preview Controller for Continuous-Time Systems

Cited by 40 publications

References 4 publications

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

H_∞optimal preview tracking control problem with disturbance attenuation

Design of zero‐sum game‐based H∞$$ {H}_{\infty } $$ optimal preview repetitive control systems with external disturbance and input delay

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Design of an Optimal Preview Controller for Continuous-Time Systems

Cited by 40 publications

References 4 publications

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

H∞optimal preview tracking control problem with disturbance attenuation

Design of zero‐sum game‐based H∞$$ {H}_{\infty } $$ optimal preview repetitive control systems with external disturbance and input delay

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H_∞optimal preview tracking control problem with disturbance attenuation