Singular Swarm Systems Research Articles

Formation tracking for singular swarm systems subjected to energy constraints and switching transmission topologies

AbstractThis article investigates admissible formation tracking for singular swarm systems under conditions of switching transmission topologies as well as the limited energy supply, where both switching transmission topologies containing a spanning tree and switching transmission topologies containing a joint spanning tree are addressed. First, a new formation control tracking protocol with switching transmission topologies is proposed to realize admissible formation tracking, where the total energy supply is predetermined. Afterwards, by a dual nonsingular transformation, the disagreement dynamics between followers and the leader is determined and the impacts of asymmetric structures of switching transmission topologies are eliminated. Sufficient conditions for admissible formation tracking design and analysis for singular swarm systems with switching transmission topologies containing a spanning tree and with switching transmission topologies containing a joint spanning tree are proposed, respectively, where the coupling relationship matrix between the total energy supply and the matrix variable is determined. Finally, two numerical simulations are presented to demonstrate the effectiveness of theoretical results.

Limited-Budget Consensus for Singular Swarm Systems With Switching Topologies

This paper investigates consensus design and analysis problems of singular swarm systems with topology switching and the given energy budget. First, a new dynamic output feedback control protocol with an energy constraint is proposed, which is singular and can make the whole swarm system satisfy some separation principle. Then, the leaderless limited-budget consensus criteria are proposed, where the gain matrices of control protocols can be designed by a new two-step design approach and an explicit expression of the consensus function is given via the First Equivalent Form, which is dependent on the dynamic modes and initial states of the whole swarm system, but is not associated with the given energy budget and protocol states. Furthermore, main consensus conclusions for leaderless cases are extended to leader-following ones, where the structures of the relationship matrices are different. Finally, the leaderless and leader-following examples are provided to demonstrate main consensus conclusions, respectively.

Admissible output consensus control for singular swarm systems

For swarm systems consisting of agents described by high-order linear singular systems, admissible output consensus problems are investigated. By using observability decomposition and eigenvalue decomposition techniques, a sufficient condition for admissible output consensus and a necessary and sufficient condition for admissible limited control energy output consensus are obtained. Furthermore, it is shown that stabilisability of the agents is a sufficient condition for admissible output consensualisability, and an approach to solve the protocol design problem is presented. Finally, a numerical example is provided to demonstrate the effectiveness of protocol design approach.

Distributed admissible consensus control for singular swarm systems with switching topologies

Summary The interaction topologies of swarm systems may be time varying due to the motions of agents or the failure of communication equipment. The current paper focuses on admissible consensus analysis and design problems for singular swarm systems with switching topologies. Admissible consensus analysis problems are converted into admissible ones of a reduced-order switching subsystem by the state projection on the consensus subspace and the complement consensus subspace. Furthermore, an approach to determine the consensus function is proposed by the first equivalent form. Moreover, by the Riccati equation, admissible consensus design criteria are presented, which can guarantee the scalability of singular swarm systems because they are independent of the number of agents. Finally, numerical examples are presented to check the correctness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

Admissible [formula omitted] consensus for singular time-delayed swarm systems with external disturbances

Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays and external disturbances are investigated. Firstly, by the state space decomposition, a necessary and sufficient condition for admissible consensus is given and an approach is presented to determine consensus functions on the basis of different impacts of initial states of agents and external disturbances, which describe the absolute motions of singular swarm systems as a whole. Then, an L2 evaluation approach which requires fewer limitations on the structures of consensus functions is proposed to determine the influences of external disturbances on relative motions among agents, and linear matrix inequality criteria for admissible L2 consensus and consensualization are shown. Finally, numerical simulations are presented to demonstrate theoretical results.

Admissible consensus analysis for high‐order linear singular swarm systems with multiple time‐varying delays and topology variances

SUMMARYAdmissible consensus analysis problems for high‐order linear time‐invariant singular swarm systems with multiple time delays and time‐varying interaction topologies are investigated. First, necessary and sufficient conditions for admissible consensus are presented, and admissible consensus problems are transformed into admissible problems of multiple lower dimensional singular systems. Then, on the basis of the first equivalent form, explicit expressions of consensus functions are given, where the impacts of initial states of agents and protocols, time delays and topology variances are determined, respectively. Moreover, it is shown that if interaction topologies are balanced, then swarm systems with the same initial states but different interaction topologies and different time delays have an identical consensus function. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays

Containment analysis and design problems for high-order linear time-invariant singular swarm systems with time delays on directed graphs are dealt with. To eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time-delayed protocols are presented for leaders and followers respectively. By model transformation, containment problems of singular swarm systems are converted into the asymptotically stable problems of multiple low-dimensional time-delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time-delayed singular swarm systems to achieve containment, which are independent of the number of agents. By applying changing variable methods, an approach is provided to determine the gain matrix in the protocols. Numerical simulations are shown to demonstrate theoretical results.

Delay-dependent admissible consensualization for singular time-delayed swarm systems

Admissible consensus analysis and design problems for high-order linear time-invariant singular swarm systems with time delays are investigated. Firstly, by state decomposition, the admissible consensus problem is transformed into admissible problems of multiple singular subsystems with lower dimensions. Then, linear matrix inequality (LMI) criteria for admissible consensualization are presented, which only involve eight LMI constraints independent of the number of agents. Moreover, an explicit expression of the consensus function which is independent of time delays is presented, and the impacts of protocol states and interaction topologies on the consensus function are revealed. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.

Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems

Admissible consensus analysis and consensualizing controller design problems for high-order linear time-invariant singular swarm systems are investigated. Firstly, by projecting the state of a singular swarm system onto a consensus subspace and a complement consensus subspace, a necessary and sufficient condition for admissible consensus is presented in terms of linear matrix inequalities (LMIs). An approach to decrease the calculation complexity is proposed, by which only three LMIs independent of the number of agents need to be checked. Then, by using the changing variable method, sufficient conditions for admissible consensualization are shown. An explicit expression of the consensus function is given, and it is shown that the modes of the consensus function can be arbitrarily placed if each agent is R-controllable and impulse controllable and the interaction topology has a spanning tree. Finally, theoretical results are applied to deal with cooperative control problems of multi-agent supporting systems.