Linear Swarm Systems Research Articles

Two‐layer distributed formation‐containment control strategy for linear swarm systems: Algorithm and experiments

SummaryThis article addresses the problem of designing a two‐layer distributed formation‐containment control scheme for linear time‐invariant swarm systems with directed communication topology, where the states of the leaders attain a prespecified time‐varying/stationary formation and the states of the followers converge into the convex hull spanned by the states of the leaders. To achieve formation‐containment, a set of distributed control protocols is developed utilizing the neighboring state information, which enables the proposed scheme operate without using global information about the entire interaction topology. The conditions to achieve formation‐containment are suggested and a theoretical proof of the proposed scheme is also derived exploiting the Lyapunov stability approach. An algorithm is written to provide systematic guidelines on how to implement the control protocols in practice. It is argued that the consensus problem, formation tracking problem, and containment control problem can all be viewed as special cases of formation‐containment. A simulation case study has been presented to demonstrate the usefulness and effectiveness of the proposed scheme and moreover, lab‐based hardware experiments involving networked mobile robots were performed to test the feasibility of the scheme in real‐time implementation.

Formation control for high-order linear swarm systems with complex communication conditions

Formation control for high-order linear swarm systems with complex communication conditions

Formation Control of High-Order Swarm Systems With Time-Varying Delays and Switching Interconnections

The paper investigates the formation control problem for high-order linear swarm systems with limited communications such as time-varying delays and switching interconnections. Firstly, the problem description is given including the dynamics of high-order swarm systems, formation protocol and the definitions of formation maintenance and tracking. Secondly, four formation conditions are derived: the former three are related to formation function, reference trajectory, auxiliary functions and network topology; the fourth one is equivalent to the stability of N-1 time-delay systems. In order to get lower conservative criteria, the Free-weighting Matrices(FWM) approach is employed to analyze the stabilization problem. Finally, the allowance upper bound of delays is calculated through solving the feasible linear matrix inequalities (LMIs). Numerical examples and simulation results are given to demonstrate the effectiveness and benefit on reducing conservativeness of the proposed method.

Distributed Time-Varying Formation Control for Linear Swarm Systems With Switching Topologies Using an Adaptive Output-Feedback Approach

Fully distributed time-varying formation (TVF) control problems are addressed in this paper using an adaptive output-feedback approach for general linear swarm systems with fixed and switching topologies. In contrast to the earlier results on formation control problems, the general linear swarm system can achieve the predefined TVF using only local output information and independent of the Laplacian matrix associated with the communication topologies. The implementation cost of calculating the global information and requiring full state information is avoided when achieving the desired TVF. First, a node-based TVF control protocol is constructed via dynamic output feedback for the case with fixed communication topology, where adaptive-based coupling weights are introduced to eliminate the dependence on the global information about the topology. Then an algorithm is presented to determine the gain matrices in the node-based adaptive TVF control protocol, and a feasible formation constraint is provided. The stability of the algorithm is proved based on the Lyapunov theory. Furthermore, under the case of switching communication topologies, an edge-based TVF control protocol is constructed with dynamic output feedback and an adaptive law for adjusting the coupling weights among agents. A sufficient condition is derived using the common Lyapunov theory for general linear swarm systems to achieve the predefined TVF satisfying the feasible formation constraint. Two numerical examples are presented to illustrate the theoretical results.

Robust H∞ Consensus Control for Linear Discrete-Time Swarm Systems with Parameter Uncertainties and Time-Varying Delays

Robust H∞ consensus control problems of linear swarm systems with parameter uncertainties and time-varying delays are investigated. In this literature, a linear consensus protocol for high-order discrete-time swarm systems is proposed. Firstly, the robust H∞ consensus control problem of discrete-time swarm systems is transformed into a robust H∞ control problem of a set of independent uncertain systems. Secondly, sufficient linear matrix inequality conditions for robust H∞ consensus analysis of discrete-time swarm systems are given by the stability theory, and a H∞ performance level γ is determined meanwhile. Thirdly, the convergence result is derived as a final consensus value of swarm systems. Finally, numerical examples are presented to demonstrate theoretical results.

Distributed Adaptive Formation Control for Linear Swarm Systems With Time-Varying Formation and Switching Topologies

In this paper, distributed time-varying formation (TVF) control problems for general linear swarm systems with switching interaction topologies are investigated using an adaptive dynamic protocol. First, a TVF control protocol for switching interaction topologies is constructed using the states of neighboring agents. In the protocol, an adaptive controller that employs gain scheduling technique is provided to estimate the coupling weights among agents. Compared with the previous studies on formation control, the desired formation can be specified by piecewise continuously time-varying differentiable vectors, the interaction topology can be switching, and the disadvantage of requiring global information of the interaction topologies is removed in this paper. Then, an algorithm including a feasible formation condition is proposed to determine the gain matrices of the distributed adaptive formation protocol by solving a linear matrix inequality for swarm systems with switching interaction topologies. Moreover, under the designed distributed adaptive formation protocol, sufficient condition for general linear swarm systems with switching interaction topologies to achieve the given TVF is derived using the Lyapunov theory. Finally, numerical simulations are presented to demonstrate the obtained results.

Uniqueness of consensus functions for time-delayed swarm systems with time-varying topologies

This paper shows that consensus functions for high-order linear swarm systems with time-varying interaction topologies and time delays are uniquely determined by initial states if interaction topologies are balanced. In addition, an explicit expression of the consensus function is presented, and the different influences of initial states of agents and protocols on the consensus function are determined respectively.

Leader–follower guaranteed-cost consensualization for high-order linear swarm systems with switching topologies

Leader–follower guaranteed-cost consensus analysis and design problems for high-order linear time-variant swarm systems with switching topologies are investigated, where two types of switching topologies are considered; that is, each interaction topology in the switching set has a spanning tree, and the union of a series of interaction topologies in a certain time interval has a spanning tree, which is referred to a joint spanning tree. Firstly, the leader–follower guaranteed-cost consensus problem is introduced, which means that all the followers in a swarm system can track the state of the leader and some performance index should be satisfied simultaneously; that is, leader–follower consensus is achieved in a suboptimal manner. Secondly, by the state decomposition, a necessary and sufficient condition for leader–follower consensus is proposed, which only transforms leader–follower consensus problems into asymptotic stability ones but cannot be directly used to determine whether or not swarm systems can achieve leader–follower consensus. Furthermore, in terms of linear matrix inequalities, sufficient conditions of leader–follower guaranteed-cost consensualization for swarm systems with a spanning tree and a joint spanning tree are presented respectively. Finally, two numerical examples are given to demonstrate theoretical results.

Time‐varying formation control for high‐order linear swarm systems with switching interaction topologies

Time-varying formation control problems for high-order linear time-invariant swarm systems with switching interaction topologies are investigated. A general formation control protocol is proposed firstly. Then using a consensus based approach, necessary and sufficient conditions for swarm systems with switching interaction topologies to achieve a given time-varying formation are presented. An explicit expression of the time-varying formation reference function is given. It is revealed that the switching interaction topologies have no effect on the formation reference function and the motion modes of the formation reference can be specified. Furthermore, necessary and sufficient conditions for formation feasibility are presented. An approach to expand the feasible formation set is given and an algorithm to design the protocol for swarm systems with switching interaction topologies to achieve time-varying formations is provided. Finally, numerical simulations are presented to demonstrate theoretical results.

Output Swarm Stability and Stabilization for High‐Order Linear Swarm Systems

AbstractOutput swarm stability and stabilization problems for high‐order linear swarm systems with directed interaction topologies are investigated. First, sufficient conditions for output swarm stability are presented, and an approach is proposed to determine the absolute output motion, where the influences of initial states of agents and swarm stabilizing protocols are given. Moreover, it is shown that swarm systems with the same initial states but different balanced interaction topologies have the same absolute output motion. Then, sufficient conditions for output swarm stabilization, which are independent of the number of agents, are presented. Finally, numerical simulations are shown to illustrate the correctness of theoretical results.

Stable‐protocol output consensus for high‐order linear swarm systems with time‐varying delays

Stable-protocol (SP) output consensus analysis and design problems for high-order linear time-invariant swarm systems with time-varying delays are investigated. First, a dynamic output feedback consensus protocol is proposed on the basis of the observable decomposition, and a necessary and sufficient condition for SP output consensus is given, which transforms the SP output consensus problem into asymptotical stability problems of multiple lower-dimensional subsystems. Then, in terms of linear matrix inequalities (LMIs), a sufficient condition for SP output consensualisation is presented, which can guarantee the scalability of swarm systems since it includes only five LMI constrains independent of the number of agents. Furthermore, an explicit expression of the output consensus function, which is independent of the time-varying delay, is shown and the impacts of initial states of agents and consensus protocols on the output consensus function are determined, respectively. Finally, a numerical example is given to demonstrate theoretical results.

Output consensus analysis and design for high-order linear swarm systems: Partial stability method

Output consensus analysis and design problems for high-order linear time-invariant swarm systems with directed interaction topologies are investigated. Firstly, as foundations of our approaches, several conclusions about partial stability are given. Then, two subspaces of the output space of swarm systems, namely an output consensus subspace and a complement output consensus subspace, are introduced. Based on output projection onto the two subspaces and partial stability, necessary and/or sufficient conditions for output consensus and limited-control-energy consensus are proposed respectively, an explicit expression of the output consensus function is presented based on the different contributions of initial states of agents and protocols, and an approach independent of the number of agents is shown to determine the gain matrices of output consensus protocols. Finally, a numerical example is given to demonstrate the theoretical results.

Consensus analysis and design for high-order linear swarm systems with time-varying delays

Consensus analysis and design problems for high-order linear time-invariant swarm systems with time-varying delays are dealt with. First, a consensus subspace and a complement consensus subspace are introduced. By the state projection onto the two subspaces, consensus problems are converted into simultaneous stabilization problems of multiple time-delayed subsystems with low dimensions, and a method to analyze and design the consensus function is given. Then, sufficient conditions for consensus and consensualization are presented, which include only four linear matrix inequality constraints. Finally, theoretical results are applied to deal with cooperative control problems of multi-agent supporting systems.