Search

This paper concerns the problem of formation‐containment control for general‐linear multi‐agent systems (MASs) with both communication delays and switching interaction topologies. On the one hand, the leaders can communicate with each other to form the desired formation and on the other, the followers need to enter the convex envelope spanned by the multiple leaders. Firstly, by using the neighbouring relative information, formation‐containment protocols are designed for each leader and follower, where an edge‐based state observer is incorporated into the formation‐containment controller to evaluate the whole leaders' state. Secondly, according to the linear matrix inequality technology, an algorithm is given to determine the unknown feedback matrixes in the protocol. Then, based on Lyapunov theory, the formation‐containment error is proved to be convergent and formation feasibility conditions are also presented for the MASs to achieve formation‐containment. Finally, a simulation on several MASs is provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Containment control problems for general linear multiagent systems with switching interaction topologies and time‐varying delays are studied. Firstly, state observers are constructed to estimate the multiple leaders under the influence of switching graphs and time‐varying delays. Secondly, a predefined containment protocol is presented based on the distributed state observer, where the expected convex combination of multiple leaders is predefined by several given weights. Moreover, an algorithm with two steps to confirm the gain matrices of the containment protocol and state observer is given. Based on linear matrix inequality technique and common Lyapunov‐Krasovskii stability theory, the convergence of this control strategy for multiagent systems with switching topologies and time‐varying delays to achieve state containment is proved. Finally, a numerical simulation is given to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the time‐varying output formation tracking (OFT) problems for linear heterogeneous multiagent systems with multiple leaders, where both the followers and the leaders can have nonidentical dynamics and dimensions. The existing results on formation tracking with multiple leaders depend on the assumption that each follower is well‐informed or uninformed, where the well‐informed follower has all the leaders as its neighbor. To remove this assumption, a novel OFT approach is presented using a distributed observer scheme. Firstly, based on the local estimation and the interaction with neighboring followers, a fully distributed observer is designed for each follower to estimate the dynamical matrices and the states of multiple leaders without requiring the well‐informed follower assumption. The convergence of the distributed observer is proved by using Lyapunov theory. Then, an adaptive algorithm is proposed to solve the regulator equations in finite time based on the estimation of the leaders' dynamical matrices. Furthermore, the desired time‐varying output formation of each follower is generated by a local active exosystem. A time‐varying OFT protocol is presented using the estimated states of multiple leaders, the online solutions of the regulator equations, and the desired formation vector generated by the local exosystem. It is proved that the outputs of the followers can not only realize the expected formation shape but also track the predefined convex combination of multiple leaders. Finally, a simulation example is given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]