Distributed finite‐time tracking control for multiple uncertain Euler–Lagrange systems with input saturations and error constraints

Chen, Liangliang; Li, Chuanjiang; Sun, Yanchao; Ma, Guangfu

doi:10.1049/iet-cta.2018.5802

Cited by 25 publications

(12 citation statements)

References 57 publications

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“…Thus, we need to tune the parameters

ϑ_{i}

and

λ_{i}

appropriately in compromise among the rapidity, tracking error and smoothness. The parameters

υ_{i}

and

F_{i}

in the adaptive law also need to be tuned to keep a balance between the learning rates and final formation tracking error. Remark 11 Since the necessary Assumption 3 is made to satisfy the condition of universal approximation theorem that

f_{i} false(x_{i} false)

is approximated by RBFNNs over a compact set, the results of this paper are not global. Remark 12 Actually, ensuring the tracking error in a desired range is of great significance and meaningfulness in practice since the better transient and steady‐state performance and communication could be obtained [31, 47, 48]. Similar to [31], the following tan‐type barrier Lyapunov function can be adopted to constrain the formation tracking errors in a predefined range.

V_{b i} = \frac{k_{b i}^{2}}{π} \tan (\frac{π e_{i, 1}^{T} e_{i, 1}}{2 k_{normalb i}^{2}})

…”

Section: Formation Tracking Control Scheme Designmentioning

confidence: 99%

“…However, the linear parameterisation‐based adaptive methods require that the uncertainty terms can be parameterised and the regressor matrixes, which are known in advance, satisfy the peresistently exiciting (PE) condition, which is really critical in practice. Therefore, as a universal approximator, neural network (NN) which is independent of prior knowledge and only requires the estimated functions to be smooth on the compact sets, is increasingly applied to compensate the unknown uncertainties, and fruitful results are obtained in the consensus or formation control for multi‐agent systems [29–31]. Nevertheless, there is a common problem that too many parameters need to be updated online in the adaptive laws in all the aforementioned results, which may be burdensome and time consuming in practice.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fixed‐time observer based adaptive neural network time‐varying formation tracking control for multi‐agent systems via minimal learning parameter approach

Xiong

et al. 2020

IET Control Theory & Applications

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“…Thus, we need to tune the parameters

ϑ_{i}

and

λ_{i}

appropriately in compromise among the rapidity, tracking error and smoothness. The parameters

υ_{i}

and

F_{i}

f_{i} false(x_{i} false)

V_{b i} = \frac{k_{b i}^{2}}{π} \tan (\frac{π e_{i, 1}^{T} e_{i, 1}}{2 k_{normalb i}^{2}})

…”

Section: Formation Tracking Control Scheme Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fixed‐time observer based adaptive neural network time‐varying formation tracking control for multi‐agent systems via minimal learning parameter approach

Xiong

et al. 2020

IET Control Theory & Applications

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“…In many practical applications, the fast convergence rate, as an important performance index in evaluating the control performance of the system, is required in the robotic manipulator control. In recent years, many efforts have been devoted to this issue, such as the finite/fixed‐time control 9‐19 . In Reference 15, the terminal sliding‐mode control scheme was designed for the robotic systems to realize the finite‐time convergence.…”

Section: Introductionmentioning

confidence: 99%

Fixed‐time cooperative control for robotic manipulators with motion constraints using unified transformation function

Liu

Zhang

Wang

et al. 2021

Intl J Robust & Nonlinear

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This article investigates the fixed‐time consensus tracking control problem for multiagent systems composed of uncertain l‐link robotic manipulators with position and velocity constraints. Fuzzy logic systems are employed to model the uncertain dynamic of the robotic manipulators. In order to cope with the asymmetric yet time‐varying constraints, a nonlinear transformation function is introduced. With the help of the nonlinear transformation function, the original constrained manipulator systems are converted into the equivalent systems without constraint. As long as the boundedness of the state variables in the transformed systems is ensured, the constraint conditions of the original systems are not violated. Then, a fixed‐time adaptive fuzzy control scheme is developed. Under the proposed control method, the consensus tracking error can converge into a small neighborhood of origin in fixed‐time, and all the signals in the closed‐loop systems are bounded. Meanwhile, the motion constraints are not violated all the time. Specially, in view of the property of nonlinear transformation function, it is not necessary to change the control structure when the systems are subjected to no state constraint. Finally, a simulation is presented to illustrate the feasibility and effectiveness of implementing the proposed control algorithms.

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“…By designing a distributed finite‐time sliding‐mode estimator, Li et al 24 investigated the distributed attitude coordinated tracking problem for multiple spacecraft systems with attitude constraints and model uncertainties. However, the finite time problem was not considered in the work of Li et al 24 In the work of Chen et al, 25 the distributed finite‐time tracking control was considered for multiple uncertain Euler‐Lagrange systems with input saturations and error constraints. However, neither of the models discussed belong to high‐order nonlinear multiagent systems with the powers of positive odd rational number.…”

Section: Introductionmentioning

confidence: 99%

Distributed finite‐time output consensus tracking for a class of high‐order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints

Liu

Wang

Ding

2020

Intl J Robust & Nonlinear

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This article considers the distributed finite-time output consensus tracking problem for a class of high-order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints. First, since the finite-time tracking design method for a single system with the powers of positive odd rational numbers cannot be extended to the finite-time consensus tracking for multiagent systems, an especial configuration method of the powers is constructed. Second, a new exponential brake function (EBF) that purely depends on the outputs is proposed to address the asymmetric output constraints directly. By adjusting a related parameter, the large converted value can be avoided when the output approaches the constrained boundaries, which may reduce the control input over a large output scale. Third, given some reasonable assumptions, a distributed finite-time output consensus tracking controller is proposed to guarantee that the tracking error converges to an adjustable small region around the origin in a finite time and that the output constraints of all subsystems are not violated. The result with output constraints can also be extended to the case without output constraints. Finally, simulation verifications also confirm the benefits and effectiveness of the proposed control methods.

show abstract

Distributed finite‐time tracking control for multiple uncertain Euler–Lagrange systems with input saturations and error constraints

Cited by 25 publications

References 57 publications

Fixed‐time observer based adaptive neural network time‐varying formation tracking control for multi‐agent systems via minimal learning parameter approach

Fixed‐time observer based adaptive neural network time‐varying formation tracking control for multi‐agent systems via minimal learning parameter approach

Fixed‐time cooperative control for robotic manipulators with motion constraints using unified transformation function

Distributed finite‐time output consensus tracking for a class of high‐order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints

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