Necessary and sufficient conditions for average formation tracking of second-order multi-agent systems with multiple leaders

Hua

et al. 2019

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Summary Time‐varying formation feasibility and formation reference function of linear multiagent systems with both time‐varying delays and switching directed topologies are studied. For a given linear multiagent system, not all the time‐varying formations can be realized due to the dynamic restriction of each agent. The formation feasibility constraint reveals the requirement on the desired time‐varying formation to be compatible with the agent dynamics. Formation reference is a representation for the macroscopic movement of the whole multiagent system. Novel features of the formation feasibility constraint and the formation reference are the main focus of this paper. Firstly, a time‐delayed formation control protocol with switching directed topologies is constructed using local neighboring information. Then, a time‐varying formation feasibility constraint is derived based on nonsingular transformations. It is proven that the time‐varying formation feasibility constraint is independent of the time‐varying delays and the switching directed topologies. Moreover, an explicit expression of the formation reference function is proposed. It is shown that neither the time‐varying delays nor the switching directed topologies has influence on the obtained formation reference function. Finally, comparative examples are provided to demonstrate the obtained results.

\overset{h}{true} false(t false)

are uniformly continuous is also necessary in related works .…”

Section: Resultsmentioning

confidence: 99%

On time‐varying formation feasibility and reference function of time‐delayed linear multiagent systems with switching digraphs

Hua

et al. 2019

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“…Remark In the works of Dong et al,() although time‐varying formation tracking problems with multiple leaders were studied, there were no nonlinearities, disturbances, and leaders' control inputs. Note that, in the work of Wang et al, only consensus control problems with disturbances were investigated by using a distributed observer.…”

Section: Resultsmentioning

confidence: 99%

“…In many practical applications, special task may need the followers to track the average state or other state forms of the multiple leaders, such as the cooperative working of the multiple manned/unmanned aerial vehicles. 34 Therefore, the formation tracking with multiple leaders is the third challenge. Dong et al 34,35 investigated the time-varying formation tracking problems with multiple leaders for second-order and high-order multi-agent systems, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…In the process of modeling the system, one can use some sensors to measure the information of the system to get the nominal model of the nonlinearity

{\overset{f}{true}}_{i} false(φ_{i} false(t false) false)

. If f i ( φ i ( t ))≡0, δ i ( t )≡0, and u k ( t )≡0, models and become the ones in the works of Dong et al() Therefore, the model studied in this this paper is general and practical.…”

Section: Preliminaries and Problem Descriptionmentioning

confidence: 96%

“…If N − M =1 and the control input of the leader u k ( t )≡0, the protocol becomes the ones in the works of Wang et al and Ding, which can only process the uncertainty nonlinearities/disturbances. If f i ( φ i ( t ))≡0, δ i ( t )≡0, and u k ( t )≡0, the protocol in the work of Dong and Hu becomes the special case of protocol . Therefore, the distributed disturbance observer‐based protocol can be applied to deal with more cooperative control problems for multiagent systems with nonlinearities and disturbances.…”

Section: Preliminaries and Problem Descriptionmentioning

confidence: 99%

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Practical time‐varying formation tracking for high‐order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

Liang

et al. 2018

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Summary Practical time‐varying formation tracking analysis and design problems for high‐order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time‐varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time‐varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer‐based practical time‐varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well‐informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time‐varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time‐varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed‐loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.

Time‐varying group formation‐tracking control for general linear multi‐agent systems with switching topologies and unknown input

et al. 2022

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Time-varying group formation tracking problems for general linear multi-agent systems with unknown control input and switching topologies are studied. There are two kinds of agents, leaders and followers. Leaders with unknown control input can generate unpredictable and maneuverable trajectories. Followers accomplish macroscopic moving guided by single or multiple leaders of respective subgroups and keep desired time-varying sub-formations simultaneously. Agents are assigned in groups and interactions within or between groups both exist owning to the design of Laplacian matrix. First, the time-varying group formation tracking problem is described and group division is analyzed through adjustment of properties in Laplacian matrix. Then the control protocols based on neighboring interaction relationships are introduced. Influence of unknown control input from leaders can be handled and information is delivered effectively so that followers can accomplish expected formations. An algorithm is given to determine control parameters and the formation tracking feasible constraint is presented. Next the stability of the multi-agent system with group division is proved, which means the general linear multi-agent system can accomplish time-varying group formation tracking with unknown control input and switch topologies under designed protocols. At last, a numerical simulation is given to verify the effectiveness of presented theoretical results.