Abstract
For high-order linear networked systems with switching topologies and the random communication silence, energy-constraint output formation problems are investigated. Firstly, the dynamics associated with the coordinated output is decomposed from the whole dynamics of each intelligent agent and a new control protocol is constructed on the basis of the coordinated outputs and the protocol states of neighboring intelligent agents, where switching topologies, the energy constraint and the random communication silence are contained. Then, by introducing the silent rate and the dwell time, the impacts of the random communication silence and switching topologies are dealt with and sufficient conditions for energy-constraint output formation design and analysis are proposed, where the output formation feasible conditions are required to guarantee the output formation achievement property. Especially, an explicit expression of the output formation center function is determined, which depicts the whole motion of a networked system when energy-constraint output formation is achieved. Finally, a numerical example is given to demonstrate theoretical conclusions.
Highlights
In the past few year, many researchers from different areas focused on networked systems consisting of multiple intelligent agents, which have many potential applications, such as flocking [1]–[3], cooperative remote sensing [4]–[6], synchronization analysis [7]–[10] and formation control [11]–[14], etc
According to the difference of the coordinated variables, distributed formation control can be divided into the state formation control and the output formation control, where it is required that all states achieve formation for the state formation case, but it is only needed that some states or combinations of states realize
For high-order linear networked systems with the energy constraint, the current paper focuses on time-varying output formation design and analysis problems, where the communication topology is randomly silent and switching
Summary
In the past few year, many researchers from different areas focused on networked systems consisting of multiple intelligent agents, which have many potential applications, such as flocking [1]–[3], cooperative remote sensing [4]–[6], synchronization analysis [7]–[10] and formation control [11]–[14], etc. Theorem 2: Under Assumptions 1-3, for any given Jmax > 0, Ku and Kζ , networked system (1) with control protocol (3) achieves energy-constraint output formation if Fcfi(t) = 0, A11fi(t) = fi(t) (i = 1, 2, · · · , M ), β(1 − ω ) > γ ωeγ ωtmax with γ > 0 and β > 0 and there exist RT = R > 0 and W T = W > 0 such that 1 = yTc (0) IM − M −11M 1TM ⊗ Ih+κ. Remark 3: For networked systems with the random communication silence and switching topologies, the whole dynamics can be divided into two independent components as shown in (10) and (11), where subsystem (10) is used to determine the output formation center function and subsystem (11) is applied to give the output formation design and analysis criteria. The random communication silence and switching topologies do not impact the whole output motion if networked systems achieve energy-constraint output formation, but the silent rate of the random communication silence and the dwell time of switching topologies are required to satisfy some constrained conditions for networked systems to realize energy-constraint output formation
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