Distributed Time-Varying Formation Tracking Analysis and Design for Second-Order Multi-Agent Systems

Hua

et al. 2019

Self Cite

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

Self Cite

“…Besides, the topologies in other works [22][23][24] were undirected, and the numbers of leaders in other works [14][15][16][17][22][23][24] were limited to be one. Although time-varying formation tracking problems were investigated in the works of Dong et al, 25,26 the systems were only limited to be second-order linear cases and there was only 1 leader. The desired formation and the dynamics of each agent in this paper are more general.…”

Section: Discussionmentioning

confidence: 99%

“…If N − M = 1, Definition 2 becomes the one to describe the time-varying formation tracking with one leader in other works. [25][26][27] If h i (t) ≡ 0, the definition of the time-varying formation tracking become the one of the consensus tracking in other works. [30][31][32][33] In practical application, it is hard to achieve the asymptotic time-varying formation tracking proposed in other works 25,26,34,35 due to the uncertain nonlinearities/disturbances and the unknown control inputs of the leaders.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…If = 0, Definition 2 becomes the definition of the asymptotic time-varying formation tracking in other works. 25,26,34,35 Therefore, Definition 2 has generality.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…From Algorithm 1, it can be shown that not all the time-varying formations can be achieved by multiagent system described by (6) using the practical time-varying formation protocol (8). The desired time-varying formation should satisfy the formation feasibility condition (11) depending on the dynamics of each agent, which means that the desired formation must be compatible with the dynamics of each agent (for more details, reader can refer to the works of Dong et al 25,26,34,35 ). The matrix K 1 is a gain matrix, which can be utilized to extend the optionality of the time-varying formation formed by the followers.…”

Section: Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

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

Liang

et al. 2018

Self Cite

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

Self Cite

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.