Dynamic leaders’ containment control of high-order multi-agent systems with state time-delay: an LMI approach

Parsa, Mohsen; Danesh, Mohammad

doi:10.1080/00207179.2016.1214880

Cited by 11 publications

(7 citation statements)

References 28 publications

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“…Definition 1: (Parsa and Danesh, 2017) Any set K ⊆ R q × 1 is said convex, if ( 1 − γ ) υ + γ ω ∈ K in which υ , ω ∈ K and γ ∈ [ 0 , 1 ] .…”

Section: Preliminariesmentioning

confidence: 99%

“…Definition 2: (Parsa and Danesh, 2017) Convex hull of a set of points such as z 1 , z 2 , … , z m ∈ R q × 1 is the minimal spanning convex set of all points z i , i = 1 , 2 , … , m . This set is represented as Co { z 1 , z 2 , … , z m } , where Co { z 1 , z 2 , … , z m } = { ∑ i = 1 m σ i z i | σ i ∈ R , σ i ⩾ 0 , ∑ i = 1 m σ i = 1 } …”

Section: Preliminariesmentioning

confidence: 99%

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High order robust fast finite time containment control for multi-agent systems

Fattahi

Zekri

Danesh

2019

Transactions of the Institute of Measurement and Control

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This paper studies the problem of robust containment with trivial sensitivity to both initial conditions and communication topology for multi-agent systems. In this way, based on the homogeneity property of the dynamic systems, a new nonlinear high order sliding surface for containment problem is proposed. This sliding surface has a fast finite time dynamics which causes remarkably reduction of containment sensitivity to the multi-agent initial conditions and communication topology. Accordingly, a high order fast finite time containment control (HOFFT-CC) protocol is established and the containment of multiple agents to a convex hull is realized. The proposed framework solves the fast containment problem for high order dynamics that are subjected to the external disturbance and furthermore, for both directed and undirected graph topology. Moreover, because of decoupling the agents’ dynamics and converting the multi-agent problem to some single agent problems, the structure of the proposed method is simpler and more straightforward in comparison with previous works. The finite time stability of the closed loop multi-agent systems based on the homogeneity theory and Lyapunov theorem, is analyzed and proved. The proof is produced throughout the negative degree homogeneity property of the closed loop dynamics along with asymptotical stability. In addition, simulation for a general third order multi-agent system in a two-dimensional space is accomplished and the results demonstrate the trivial sensitivity of containment to both initial conditions and communication topology.

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“…Definition 1: (Parsa and Danesh, 2017) Any set K ⊆ R q × 1 is said convex, if ( 1 − γ ) υ + γ ω ∈ K in which υ , ω ∈ K and γ ∈ [ 0 , 1 ] .…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

High order robust fast finite time containment control for multi-agent systems

Fattahi

Zekri

Danesh

2019

Transactions of the Institute of Measurement and Control

Self Cite

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show abstract

“…The containment control methods have been studied from different perspectives in the literature [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Dong et al presented formation-containment controller for multiagent systems with directed topologies [39,40].…”

Section: Introductionmentioning

confidence: 99%

Distributed adaptive containment control for a group of aerial robots with external disturbances

Arab

Shirazi

Yazdi

2021

Asian Journal of Control

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A novel distributed containment control for multiple quadrotor agents under a fixed topology graph is addressed in this paper. There are two layers in the containment control problem. Communication graph, information of leaders, and neighbors of each follower are used to determine the desired trajectory for followers in the first layer. In the second layer, each follower should use the information of itself and its neighbors to follow the desired trajectory. The tracking control algorithm of followers has two subsystems with a cascade structure: the translational and the rotational dynamics of the agents. The distributed containment controller is utilized for the outer‐loop to track the desired trajectory based on the invariance and immersion adaptive control in order to compensate the external disturbances. For the inner loop, an adaptive control algorithm is designed to follow the desired attitudes obtained from the translational dynamics. In the end, the simulation results are provided for three scenarios to verify the performance of the presented control scheme in the presence of the external disturbances.

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“…“sign” function) protocols that can result in undesired problems, for example, chattering phenomena. Unlike the mentioned approaches, in [16,17] the leaders are dynamic but the control protocols are smooth. In these studies, the leaders can have different dynamics (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, this model can cover different cases such as multi‐agent systems comprised of mobile robot, single‐link joint manipulators, inverted pendulums (with limited variation around the linearization point), mass‐spring‐damper systems, and RLC oscillators. This study investigates the dynamic leader containment control problem with polynomial‐type trajectories and applies a smooth PI‐type protocol; however, one of the main contributions of this paper is that it develops the protocol in [16,17] such that the proposed protocol benefits from a flexible combination of a local state feedback and a distributed PI‐type controller. As a result, this protocol does not need to access all elements of the containment error vector.…”

Section: Introductionmentioning

confidence: 99%

Containment control of high‐order multi‐agent systems with heterogeneous uncertainties, dynamic leaders, and time delay

Parsa

Danesh

2019

Asian Journal of Control

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This paper deals with containment control of multi‐agent systems where high‐order canonical controllable linear systems with heterogeneous uncertainties are considered as the agents' dynamics. The leaders are dynamic with polynomial‐type trajectories. In this paper, the control protocol is smooth and it is constructed from a flexible combination of local state feedback controller and a PI‐type protocol. Utilizing this protocol, containment without suffering from chattering phenomena and consideration of any bound on the agents' states is achieved. In addition, the flexibility of this protocol helps the designer to reduce or even discard the inter‐agent communication. Recalling the significant effects of time delay on the performance and stability of multi‐agent systems, in this paper input time delay is also considered. Following a Lyapunov‐Krasovskii stability approach, two linear matrix inequalities (LMIs) are derived, and then solving the LMIs' gains of the protocol are attained such that asymptotic stability of the multi‐agent system under switching graph topology is guaranteed. Finally, the feasibility of the LMIs and the validity of the theoretical results are demonstrated through some numerical examples.

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Dynamic leaders’ containment control of high-order multi-agent systems with state time-delay: an LMI approach

Cited by 11 publications

References 28 publications

High order robust fast finite time containment control for multi-agent systems

High order robust fast finite time containment control for multi-agent systems

Distributed adaptive containment control for a group of aerial robots with external disturbances

Containment control of high‐order multi‐agent systems with heterogeneous uncertainties, dynamic leaders, and time delay

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