Optimal tracking control for nonlinear large-scale systems with persistent disturbances

Tang, Ruichun; Lü, Xianmin; Zhai, Yili; Gong, Cunqun

doi:10.1007/s11768-010-8033-2

Cited by 2 publications

(7 citation statements)

References 9 publications

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“…is means that (E i , A i ) is regular and impulse free [26]. In addition, the right side of the two formulas is denoted as E i and A i , respectively, i.e., E i � S i E i T i � I p+q i 0 0 0 and (12), introducing a nonsingular linear transformation X i (t) � T i X i (t) and then premultiplying a nonsingular matrix S i on both sides, we obtain…”

Section: Controller Of the Error System Of Isolated Subsystemsmentioning

confidence: 99%

“…Next, the optimal preview controller for System (12) and the performance index (13) is given. Firstly, the following two lemmas are established.…”

Section: Controller Of the Error System Of Isolated Subsystemsmentioning

confidence: 99%

“…is detectable, and A6 holds; then under the performance index function (13), the optimal preview controller of System (12) is…”

Section: Theorem 2 If (E I a I ) Is Regular And Impulse Freementioning

confidence: 99%

“…erefore, the controller (24) is obtained according to eorem 1. Because T i is an invertible matrix in the transformation X i (t) � T i X i (t), the optimal preview controller (24) for System (21a) and the performance index 23is the optimal preview controller for System (12) under the performance index function (13).…”

Section: Proofmentioning

confidence: 99%

“…e controllers satisfying the requirements are designed, respectively. en, the controller of the interconnected system is obtained through a certain method of synthesis [12,13]. In recent years, there exist many research studies on control theory of singular interconnected systems and many significant results have been obtained [14,15].…”

Section: Introductionmentioning

confidence: 99%

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Preview Tracking Control for Continuous-Time Singular Interconnected Systems

Xie

Liao

Deng

2019

Mathematical Problems in Engineering

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This paper proposes and investigates a problem of preview tracking control for a class of continuous-time singular interconnected systems. Firstly, the related items are deleted to obtain several isolated subsystems with low dimensions. An error system is constructed for each isolated subsystem so that the tracking error is included in the state vector of the error system; then, the tracking problem is transformed into a regulation problem. Secondly, the preview tracking controller is designed for each error system and obtained controllers are combined as the controller of the error system of the singular interconnected system. Thirdly, the Lyapunov function method is utilized to determine the constraints of the related terms so that the closed-loop system of the error system of the singular interconnected system is stable under the action of the controller obtained. Finally, the preview tracking controller of the singular interconnected system is obtained from the relationship between the error system and the original system. A numerical simulation algorithm for continuous-time singular systems is also proposed in this paper. The numerical simulation illustrates the effectiveness of the theoretical results.

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Section: Controller Of the Error System Of Isolated Subsystemsmentioning

confidence: 99%

“…Next, the optimal preview controller for System (12) and the performance index (13) is given. Firstly, the following two lemmas are established.…”

Section: Controller Of the Error System Of Isolated Subsystemsmentioning

confidence: 99%

“…is detectable, and A6 holds; then under the performance index function (13), the optimal preview controller of System (12) is…”

Section: Theorem 2 If (E I a I ) Is Regular And Impulse Freementioning

confidence: 99%

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Preview Tracking Control for Continuous-Time Singular Interconnected Systems

Xie

Liao

Deng

2019

Mathematical Problems in Engineering

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Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

2020

Complexity

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In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

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Optimal tracking control for nonlinear large-scale systems with persistent disturbances

Cited by 2 publications

References 9 publications

Preview Tracking Control for Continuous-Time Singular Interconnected Systems

Preview Tracking Control for Continuous-Time Singular Interconnected Systems

Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

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