Robust adaptive uniform exact tracking control for uncertain Euler–Lagrange system

Yang, Yana; Chen, Hua; Li, Junpeng; Guan, Xinping

doi:10.1080/00207179.2016.1263761

Cited by 19 publications

(27 citation statements)

References 27 publications

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“…In inequality (32), the fact that −(x 1 + x 2 ) ≤ −(x 1 + x 2 ) + 2, where x 1 , x 2 ≥ 0 and > 1, and Lemma 2 are utilized. With V(0) > 0,V ≤ −ΥV +̄, multiplying e t yields d dt V(t)e Υt ≤ e Υt̄; integrating this function over [0, t], we have V(t) ≤Ῡ + V(0); and it is obvious that V(t) is bounded.…”

Section: Figure 4 Compact Sets In Theoremmentioning

confidence: 99%

“…First, define sets Ω X 0 = {|{X |||X || < R (0, X (0), 0, 0)} ∈ Ω X }, which are not empty. Then, for the system with X (0) ∈ Ω X 0 , bounded̂(0),̂(0), the following constants can be determined by Ξ = sup (32), we know that, if the adaptive control parameters m1 and s1 are chosen to be sufficiently small, Λ m , Λ s , Δ m and Δ s are taken to be sufficiently large, then the constantῩ can be made arbitrary small, for the initial condition X (0) ∈ Ω X 0 , bounded̂(0),̂(0), if the adaptive control parameters are appropriately chosen such thatῩ ≤ Ξ, then the system state X j indeed stays in Ω X for all the times. The proof is completed.…”

Section: Figure 4 Compact Sets In Theoremmentioning

confidence: 99%

“…Considering this problem, based on the FTSM control theory, several new results based on the notion fixed-time stability 28,29 have appeared recently by focusing on designing fixed-time controllers for linear-system, 29 consensus tracking controllers for multiple nominal double integrator networks, 30 nonlinear interconnected systems, 31 and uncertain Euler-Lagrange system. 32 In this paper, new fixed-time control approaches will be proposed for nonlinear bilateral teleoperation system in the presence of system parameter uncertainties and external disturbances. A complicated situation that the bilateral teleoperation system composed of a single-master and multiple-slave handling an object in operational space is considered.…”

Section: Introductionmentioning

confidence: 99%

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Multi‐manipulators coordination for bilateral teleoperation system using fixed‐time control approach

Yang

Chen

Guan

2018

Intl J Robust & Nonlinear

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Summary In this paper, the fixed‐time synchronization control problem for bilateral teleoperation system composed of a single master manipulator and multiple cooperative slave manipulators with system uncertainties and external disturbances is addressed. The multiple cooperative slave manipulators have the capability to perform some complex tasks that are difficult or even impossible to be executed by a single slave manipulator. In order to control the multiple slave manipulators handling a common object with faster speed and higher accuracy, a new adaptive neural networks (NNs)–based fixed‐time control scheme is proposed. First, under the assumptions that the slave manipulators are rigidly grasping a nondeformable object, an integrated dynamic model composed of multiple slave manipulators and an object is derived. The object's grasping forces are concealed in the derived dynamics and can be controlled independent of the motion space. Then, a new nonsingular integral terminal sliding mode providing fixed‐time convergence of the velocity and position errors is designed with high‐degree terms and lower‐degree terms. By setting proper initial value of the integral function, the system settling time will be reduced greatly. Moreover, the corresponding adaptive NN‐based fixed‐time control approach is proposed by employing the strong approximation of the NNs. It is proved that the closed‐loop teleoperation system is semiglobally fixed‐time stable and the synchronization errors between the local manipulator and the object will converge to zero in fixed time for any initial condition of the master and the slaves. Finally, simulation and experiment are both performed to verify the effectiveness of the proposed method.

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Section: Figure 4 Compact Sets In Theoremmentioning

confidence: 99%

Section: Figure 4 Compact Sets In Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi‐manipulators coordination for bilateral teleoperation system using fixed‐time control approach

Yang

Chen

Guan

2018

Intl J Robust & Nonlinear

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“…Due to the advantage of the conventional sliding mode control, the closed‐loop system is insensitive to the parameter perturbation and external disturbance only during the sliding phase. For the sake of improving the robustness of the whole system, the integral sliding mode control that can eliminate the reaching phase of the conventional sliding mode control was widely applied in EL systems . Tho et al investigated a robust integral sliding mode controller that can make the system slide on the sliding surface at the very beginning of the motion for an underactuated rotary hook system.…”

Section: Introductionmentioning

confidence: 99%

“…In order to weaken the chattering phenomenon, Lee et al proposed an adaptive robust controller for robot manipulators using the adaptive integral sliding mode control and time delay estimation. To get the rapider speed of convergence, Yang et al designed an adaptive finite‐time controller for an uncertain EL system via a nonsingular integral terminal sliding mode surface.…”

Section: Introductionmentioning

confidence: 99%

Integral sliding mode control for Euler‐Lagrange systems with input saturation

Guo

Huang

2018

Intl J Robust & Nonlinear

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This paper investigates the robust control for the Euler-Lagrange (EL) system with input saturation by using the integral sliding mode control and adaptive control. An integral sliding mode surface that is suitable for solving the problem of the input constraint is given based on the saturation function. By using the integral sliding mode surface, two robust antisaturation controllers are designed for the EL system with external disturbances. The first controller can deal with the external disturbances with known bounds, whereas the second one can compensate the external disturbances with unknown bounds by using the adaptive control. Finally, the effectiveness of the proposed controllers is demonstrated by strict theoretical analysis and numerical simulations. KEYWORDS adaptive control, Euler-Lagrange system, input saturation, integral sliding mode control, robust control 1088

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Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

Sun

Liu

2019

Asian Journal of Control

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An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.

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Robust adaptive uniform exact tracking control for uncertain Euler–Lagrange system

Cited by 19 publications

References 27 publications

Multi‐manipulators coordination for bilateral teleoperation system using fixed‐time control approach

Multi‐manipulators coordination for bilateral teleoperation system using fixed‐time control approach

Integral sliding mode control for Euler‐Lagrange systems with input saturation

Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

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