High-order fully actuated system approaches: Part III. Robust control and high-order backstepping

Duan, Guang‐Ren

doi:10.1080/00207721.2020.1849863

Cited by 160 publications

(54 citation statements)

References 23 publications

(30 reference statements)

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“…In the timevarying case, global stability in the sense that all the states of the system remain bounded is proven, while in the time-invariant case, global asymptotical stability is achieved. The results contain those in Duan (2021b) and Duan (2021c) as special cases.…”

Section: First-vs High-order System Approachesmentioning

confidence: 87%

“…The work in this paper is closely related to that in Part III (Duan, 2021b) and Part IV (Duan, 2021c) of the series. The problem is a combination of those in both parts, which is concerned with a type of HOFA system with both nonlinear uncertainties and unknown parameter vectors.…”

Section: First-vs High-order System Approachesmentioning

confidence: 90%

“…In Part III of this series (Duan, 2021b), we first propose a robust controller for a type of HOFA systems with nonlinear uncertainties and then develop, based on the obtained result, the high-order method of robust backstepping for second-order and high-order strict feedback systems with nonlinear uncertainties. Parallelly, in Part IV of this series (Duan, 2021c), an adaptive controller for a type of HOFA systems with a set of unknown parameters is firstly proposed, and then, based on the obtained result, a high-order method of adaptive backstepping for second-order and high-order strict feedback systems with parametric uncertainties is developed.…”

Section: First-vs High-order System Approachesmentioning

confidence: 99%

“…with ρ(x,ẋ,ẍ) being some non-negative scalar function. Different from Duan (2021c), in this example, we allow the parameter θ in system (58) to be timevarying. Applying Theorem 3.1, we obtain the robust adaptive controller for system (58) as follows:…”

Section: An Illustrative Examplementioning

confidence: 99%

“…According to Duan (2021c), in order that the matrix (A 0∼2 ) has eigenvalues −a ± jb and −c, we need to choose A 0∼2 as…”

Section: Solution Of a 0∼2 And P L (A 0∼2 )mentioning

confidence: 99%

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High-order fully actuated system approaches: Part V. Robust adaptive control

Duan

2021

International Journal of Systems Science

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112

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A type of high-order fully actuated (HOFA) systems with both nonlinear uncertainties and timevarying unknown parameters is considered, and a direct approach for the designs of robust adaptive stabilising controllers and robust adaptive tracking controllers is proposed based on the Lyapunov stability theory. The established controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed-loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, and the adaptation part adjusts online the controller to suit the effect of the unknown timevarying parameter vector. The proposed controller guarantees that the tracking error of the state to a given signal and the estimation error of the parameter vector finally converge globally into a bounded ellipsoid. Particularly, in the case that the unknown parameter vector is constant, an adaptive scheme that enables global asymptotical tracking is presented. An example demonstrates the effect of the proposed approach.

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Section: First-vs High-order System Approachesmentioning

confidence: 87%

Section: First-vs High-order System Approachesmentioning

confidence: 90%

Section: First-vs High-order System Approachesmentioning

confidence: 99%

Section: An Illustrative Examplementioning

confidence: 99%

“…According to Duan (2021c), in order that the matrix (A 0∼2 ) has eigenvalues −a ± jb and −c, we need to choose A 0∼2 as…”

Section: Solution Of a 0∼2 And P L (A 0∼2 )mentioning

confidence: 99%

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High-order fully actuated system approaches: Part V. Robust adaptive control

Duan

2021

International Journal of Systems Science

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112

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Adaptive control and almost disturbance decoupling for uncertain HOFA nonlinear systems

Wang

Liu

et al. 2023

Adaptive Control & Signal

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Summary In this paper, the problem of adaptive stability control for uncertain high‐order fully actuated (HOFA) nonlinear systems with disturbances is solved. The method of almost disturbance decoupling (ADD) is used to cope with unknown disturbances. Meanwhile, the tuning function is applied to design an adaptive update law. According to the full‐actuation feature of HOFA systems and Lyapunov stability theory, a novel adaptive controller is designed. In the end, the effectiveness of the control strategy is validated by a numerical simulation example and the attitude control of a spacecraft.

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High‐order robust command filtered backstepping design for strict‐feedback systems: A high‐order fully actuated system approach

Liu

Duan

Hou

2022

Intl J Robust & Nonlinear

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A high-order fully actuated (HOFA) system approach is invoked to construct a high-order robust command filtered backstepping (HORCFB) controller to track a feasible desired output trajectory for the second-and high-order strict-feedback systems (SFSs) subjected simultaneously to nonlinear uncertainties, where the subsystems of the SFSs possess a common full-actuation structure. Unlike the existing classical first-order state-space approach, the proposed HORCFB scheme avoids converting the high-order systems into first-order ones, and thus simpler to implement and needs fewer steps. Moreover, the presented result avoids the complexity arising due to repeatedly differentiating, namely, the problem of "explosion of complexity." Stability analysis of the closed-loop system shows that all the states of the closed-loop system are kept uniformly ultimately bounded, and the output is driven to track a feasible desired output trajectory with an arbitrarily small error by proper selection of the design parameters. Finally, the effectiveness of the proposed scheme is demonstrated by the trajectory tracking control problem of a single-link robot arm with the elastic revolute joint.

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High-order fully actuated system approaches: Part III. Robust control and high-order backstepping

Cited by 160 publications

References 23 publications

High-order fully actuated system approaches: Part V. Robust adaptive control

High-order fully actuated system approaches: Part V. Robust adaptive control

Adaptive control and almost disturbance decoupling for uncertain HOFA nonlinear systems

High‐order robust command filtered backstepping design for strict‐feedback systems: A high‐order fully actuated system approach

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