Qingdong Li

Distributed adaptive time-varying formation for multi-agent systems with general high-order linear time-invariant dynamics☆

Abstract This paper studies distributed time-varying formation control problems for general high-order linear time-invariant (LTI) multi-agent systems using an adaptive based approach. Firstly, a time-varying formation control protocol is constructed by the states of neighboring agents, which the adaptive gain scheduling technique is employed to estimate the coupling weights between neighboring agents. Different from the existing results on formation control, the formation can be specified by piecewise continuously differentiable vectors and no global information about the interaction topologies is required. Then an algorithm with two steps is presented to design the distributed adaptive formation control protocol, where a description of the feasible time-varying formation set is given. The stability of the algorithm is proved using the Lyapunov theory. It is shown that if the predefined time-varying formation belongs to the feasible formation set and each agent is stabilizable, then time-varying formation can be achieved by general high-order LTI multi-agent systems using the distributed adaptive formation protocol designed in the proposed algorithm. Finally, numerical examples are given to demonstrate the effectiveness of the theoretical results.

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

Abstract Average formation tracking problems for second-order multi-agent systems with multiple leaders and directed interaction topologies are studied, where the states of followers form a predefined time-varying formation while tracking the average state of the multiple leaders. An average formation tracking protocol is constructed using neighboring relative information, where only part of the followers which are named as well-informed ones are required to obtain the information of the multiple leaders. New properties of the Laplacian matrix are derived under the assumption that for each uninformed follower, there exists at least one directed path from a well-informed follower to it. Necessary and sufficient conditions for second-order multi-agent systems with multiple leaders to achieve average formation tracking are proposed by utilizing the properties of the Laplacian matrix. An approach to design the average formation tracking protocol is presented by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems, average tracking problems and consensus tracking problems for second-order multi-agent systems with one or multiple targets/leaders. An application example in multiple vehicles enclosing is provided to demonstrate the effectiveness of the theoretical results.

Output formation-containment analysis and design for general linear time-invariant multi-agent systems ☆

Abstract Output formation-containment control problems for general linear time-invariant multi-agent systems with directed topologies are dealt with. Output formation-containment means that the outputs of leaders achieve the predefined formation, and at the same time the outputs of followers converge to the convex hull formed by the outputs of leaders. Firstly, static output protocols are presented for leaders and followers respectively. Then output formation-containment problems of multi-agent systems are transformed into asymptotic stability problems. Sufficient conditions with less computation complexity are proposed for multi-agent systems to achieve the output formation-containment. An explicit expression for the time-varying output formation reference function is derived to describe the macroscopic movement of the whole output formation-containment. Explicit expressions to describe the relationship among the outputs of followers, the time-varying output formation for the leaders and the output formation reference are derived. It is proven that the outputs of followers not only converge to the convex hull formed by those of leaders but also achieve certain time-varying formation specified by the convex combination of the desired output formation for the leaders. Moreover, an approach to determine the gain matrices in the protocols is given for multi-agent systems to achieve the output formation-containment. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

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

Distributed time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. Different from the previous results on formation tracking control, the formation for the followers can be described by specified time-varying vectors and the trajectory of the leader can also be time-varying. A distributed formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.

Containment analysis and design for general linear multi-agent systems with time-varying delays

Containment analysis and design problems for general high-order linear time-invariant multi-agent systems with time-varying delays are studied, where the interaction topology is directed. Using the state information of each agent and neighboring agents, a protocol with time-varying delays is constructed, where the motion modes of the leaders can be specified. Based on Lyapunov-Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with time-varying delays to achieve containment are proposed which only include four linear matrix inequalities independent of the number of agents. Moreover, an approach to determine the gain matrices in the protocol is presented. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results.

Formation-containment control for second-order multi-agent systems with time-varying delays ☆

Abstract In this paper, formation-containment control problems for multi-agent systems with second-order dynamics and time-varying delays are studied. The states of leaders are designed to achieve the time-varying formation and the states of followers are required to converge to the convex hull spanned by those of leaders simultaneously, which differs from conventional formation control or containment control problems. Using the neighboring positions and velocities, formation-containment protocols with time-varying delays are constructed. By exploiting the space decomposition approach, formation-containment problems are transformed into the asymptotically stable problems. Sufficient conditions for second-order multi-agent systems with time-varying delays to realize formation-containment are presented. A method to obtain the unknown gain matrices in the protocols is proposed. Numerical simulations are shown to illustrate the effectiveness of the theoretical results.

Time-varying formation control for double-integrator multi-agent systems with jointly connected topologies

ABSTRACT Time-varying formation analysis and design problems for double-integrator multi-agent systems with jointly connected topologies are investigated. Different from the previous work on formation control, in this paper, the formation is specified by time-varying piecewise continuously differentiable vectors and the topology can be disconnected at any time instant. First, a distributed formation control protocol is constructed using local neighbour-to-neighbour information. In the case where the switching topology is jointly connected, necessary and sufficient conditions for double-integrator multi-agent systems to achieve time-varying formations are proposed, where the formation feasibility constraint is also derived. To describe the macroscopic movement of the whole formation, explicit expressions of the formation reference are presented, the motion modes of which can be partially assigned. Moreover, an approach to design the formation control protocol is given, which is fully distributed and requires no global information about the topology. Finally, the obtained theoretical results are applied to deal with the time-varying formation control problems of multi-vehicle systems.

Time-varying formation control for second-order swarm systems with switching directed topologies ☆

Abstract Formation control problems for second-order swarm systems with general directed topologies are addressed in this paper, where the desired formation can be time-varying and the directed topology can be switching. Firstly, a distributed time-varying formation control policy using local neighboring state information is proposed. Then an algorithm to design the policy with switching directed topologies is presented. Sufficient conditions for second-order swarm systems to achieve the predefined time-varying formation under the designed policy are derived based on the piecewise Lyapunov function theory, where the formation feasibility constraint and the threshold for the dwell time are proposed, respectively. Moreover, an explicit expression of the formation reference function is obtained to describe the macroscopic trajectory of the whole time-varying formation under the influence of the switching directed topologies. Finally, a numerical simulation is provided to demonstrate the effectiveness of the obtained results.

Adaptive decoupling control of hypersonic vehicle using fuzzy-neural network observer

An adaptive decoupling control approach using fuzzy-neural network (FNN) observer for a class of MIMO nonlinear systems with parameter uncertainties is presented in this article. First, a decoupling controller is constructed based on the decentralized control theory. Furthermore, the system coupling terms and uncertainties are estimated by the FNN observer and added into the control law for compensation. The FNN approximate-matrix update law and the control law guarantee that the tracking errors of the system states, the observer states and the approximate matrix are all uniformly ultimately bounded within a region that can be kept arbitrarily small. Secondly, a model for the hypersonic vehicle is given and an attitude controller is designed using the decoupling control approach. Finally, simulations are carried out on the hypersonic vehicle to demonstrate the effectiveness of the proposed method.

Time-varying formation tracking for second-order multi-agent systems with one leader

Time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.