Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems

Yang, Dapeng; Ren, Wei; Liu, Xiangdong

doi:10.1016/j.sysconle.2014.07.006

Cited by 57 publications

(62 citation statements)

References 22 publications

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“…Associated with the digraph

\overset{scriptG}{true}

, define its Laplacian matrix

L = [l_{i j}] \in {double-struckR}^{(N + m) \times (N + m)}

with

l_{i i} = \sum_{j = 1, j \neq i}^{N + m} a_{i j}

and l i j =− a i j , i ≠ j , which is defined as follows: for i = 1,⋯, N , j = 1,⋯, N + m ,

a_{i j} = ({, \begin{matrix} 1, & (j, i) \in \bar{E} \\ 0, & otherwise \end{matrix})

Note that Laplacian matrix L can be written as

L = ([], \begin{matrix} L_{1} & L_{2} \\ 0_{m \times N} & 0_{m \times m} \end{matrix})

with

L_{1} \in {double-struckR}^{N \times N}

and

L_{2} \in {double-struckR}^{N \times m}

. As in , we also need the following assumption for the communication network.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…The control objective is to design a distributed continuous control law such that, under Assumption , all the trajectories of Lagrangian systems can asymptotically converge to the convex hull spanned by heterogenous dynamic leaders given by , that is,

\lim_{t \to \infty} | | q_{i} (t) - h (t) | | = 0, i = 1, \dots, N

where i = 1,⋯, N , h ( t )∈ C o ( r ) with r = col( r N + 1 ,⋯, r N + m ), instead of ensuring || q i − h ( t )|| < σ with σ sufficiently small as in . Let

q_{d} = col (q_{d 1}, \dots, q_{d N}) = - ((), L_{1}^{- 1} L_{2} \otimes I_{n}) r

.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…Remark The first three assumptions are standard for Lagrangian systems as can be found in , and the last assumption allows exosystem to generate a large class of functions, for example, a combination of step functions of unknown magnitudes, ramp functions of unknown slopes, and sinusoidal functions of unknown amplitudes, initial phases, and unknown frequencies. It is noted that the assumption for the leader systems in requires

{\overset{v}{true}}_{i}

and v ... i to be bounded, and the bounds are known to all agents, while requires both v i and

{\overset{v}{true}}_{i}

are bounded and requires

{\overset{v}{true}}_{i}, {\overset{v}{true}}_{i}

, and v ... i to be bounded.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…Recent representative work about coordinated control of multiple Lagrangian systems includes , which proposed a discontinuous controller to make a group of agents asymptotically converge to a convex hull spanned by dynamic leaders with varying vectors of generalized coordinate derivatives, while further improved the result in the sense that it not only proposed fully distributed adaptive sliding‐mode controllers, the control gain of which was independent of the upper bound of the first and second derivatives of leaders' signals, but also considered the existence of external disturbances. Furthermore, besides a fully distributed discontinuous control law, also proposed a continuous one to make sure the tracking error was ultimately bounded; considered the containment problem for both second‐order nonlinear systems and Lagrangian systems subject to external disturbances by discontinuous adaptive control strategies with or without relative velocity feedback, which could reduce the containment errors as small as desired by tuning control gain for arbitrary bounded initial conditions. With additional condition

\lim_{t \to \infty} | | {\overset{q}{true}}_{L} (t) | | = 0, q_{L} (t)

denoting the column stack vector of leaders' signals here, the containment error could converge to zero asymptotically.…”

Section: Introductionmentioning

confidence: 99%

“…This paper studies the coordinated control with multiple leaders for Lagrangian multi‐agent systems subject to external disturbances and renders some distinguished features. The control strategy we propose here can achieve the asymptotic convergence of the containment error without any additional condition instead of ultimate boundedness like , and it is also a fully distributed self‐tuning adaptive one, depending neither on any information of leader systems for uninformed followers, nor on the external disturbances. It is worth to mention that it is also a continuous one, which can beat the inherent drawback of a discontinuous one that might result in undesired chattering effect in the real applications on switching devices . Technically, the control design we propose does not depend on the neighbors' velocity, which implies wider potential applications and promises lower cost in sensory and maintenance; instead of constant gain based on the information of communication network, dynamic gains are considered to produce a sufficiently high gain to handle unbounded certainties in the literature of adaptive control by applying the non‐identifier‐based high‐gain adaptive control technique .…”

Section: Introductionmentioning

confidence: 99%

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Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

Dong

2016

Intl J Robust & Nonlinear

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Summary This paper studies coordinated control of multiple Lagrangian systems with parametric uncertainties subject to external disturbances by proposing a fully distributed continuous control law based on the improved self‐tuning adaptive observer inspired by non‐identifier‐based high‐gain adaptive control technique. Under this distributed continuous control law, a group of Lagrangian systems are driven to the convex hull spanned by multiple heterogenous dynamic leaders, which can be any combination of step signals of arbitrary unknown magnitudes, ramp signals of arbitrary unknown slopes, and sinusoidal signals of arbitrary unknown amplitudes, initial phases, and any unknown frequencies. It is also worth to mention that this control law we propose, depending neither on any information of leader systems for uninformed followers, nor on external disturbances, even independent of neighbors' velocity, can achieve asymptotic tracking of multiple leaders without any additional condition instead of ensuring the ultimate boundedness of the containment error as in the literature. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Associated with the digraph

\overset{scriptG}{true}

, define its Laplacian matrix

L = [l_{i j}] \in {double-struckR}^{(N + m) \times (N + m)}

with

l_{i i} = \sum_{j = 1, j \neq i}^{N + m} a_{i j}

and l i j =− a i j , i ≠ j , which is defined as follows: for i = 1,⋯, N , j = 1,⋯, N + m ,

a_{i j} = ({, \begin{matrix} 1, & (j, i) \in \bar{E} \\ 0, & otherwise \end{matrix})

Note that Laplacian matrix L can be written as

L = ([], \begin{matrix} L_{1} & L_{2} \\ 0_{m \times N} & 0_{m \times m} \end{matrix})

with

L_{1} \in {double-struckR}^{N \times N}

and

L_{2} \in {double-struckR}^{N \times m}

. As in , we also need the following assumption for the communication network.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

\lim_{t \to \infty} | | q_{i} (t) - h (t) | | = 0, i = 1, \dots, N

where i = 1,⋯, N , h ( t )∈ C o ( r ) with r = col( r N + 1 ,⋯, r N + m ), instead of ensuring || q i − h ( t )|| < σ with σ sufficiently small as in . Let

q_{d} = col (q_{d 1}, \dots, q_{d N}) = - ((), L_{1}^{- 1} L_{2} \otimes I_{n}) r

.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

{\overset{v}{true}}_{i}

and v ... i to be bounded, and the bounds are known to all agents, while requires both v i and

{\overset{v}{true}}_{i}

are bounded and requires

{\overset{v}{true}}_{i}, {\overset{v}{true}}_{i}

, and v ... i to be bounded.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

\lim_{t \to \infty} | | {\overset{q}{true}}_{L} (t) | | = 0, q_{L} (t)

denoting the column stack vector of leaders' signals here, the containment error could converge to zero asymptotically.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

Dong

2016

Intl J Robust & Nonlinear

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show abstract

Robust containment control in a leader-follower network of uncertain Euler-Lagrange systems

Klotz

Cheng

Dixon

2016

Int. J. Robust. Nonlinear Control

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Summary A distributed controller is developed that yields cooperative containment control of a network of autonomous dynamical systems. The networked agents are modeled with uncertain nonlinear Euler–Lagrange dynamics affected by an unknown time‐varying exogenous disturbance. The developed continuous controller is robust to input disturbances and uncertain dynamics such that asymptotic convergence of the follower agents' states to the dynamic convex hull formed by the leaders' time‐varying states is achieved. Simulation results are provided to demonstrate the effectiveness of the developed controller. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

Cui

Chen

et al. 2018

Intl J Robust & Nonlinear

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In this paper, the problem of distributed containment control for pure-feedback nonlinear multiagent systems under a directed graph topology is investigated.The dynamics of each agent are molded by high-order nonaffine pure-feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed-loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.

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Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems

Cited by 57 publications

References 22 publications

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

Robust containment control in a leader-follower network of uncertain Euler-Lagrange systems

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

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