Abstract
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.
Highlights
Formation control of swarm systems is widely applied in surveillance and reconnaissance [1]–[3], target searching and localization [4]–[7], telecommunication relay [8], space exploration and source seeking [9], [10]
This paper mainly focusses on the formation control problem of high-order swarm systems with time-varying delays and switching topologies
We assume that h(t) and r(t) are uniform continuously differentiable. dt denotes the time-varying delays between agents
Summary
Formation control of swarm systems is widely applied in surveillance and reconnaissance [1]–[3], target searching and localization [4]–[7], telecommunication relay [8], space exploration and source seeking [9], [10]. Distributed time-varying formation control problem was discussed for high-order linear MASs with directed network by developing an adaptive outputfeedback approach [23]. The formation feasibility such as delay-independent or dependent condition is derived using the Nyquist criterion [26] or Lyapunov appraoches [27]–[31] The latter method seems better when dealing with the time-varying delays and switching topologies [32]–[35]. The formation tracking problem with time-varying delays is presented, and the protocol is derived based on the full state information [42]. This paper mainly focusses on the formation control problem of high-order swarm systems with time-varying delays and switching topologies. Both time-varying delays and switching topologies are considered. I is an identity matrix and 0 is zero matrix with appropriate dimensions
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