Due　to　the　limited　coverage　of　base　station　(BS)　and　battery　capacity　of　mobile　users,　the　resource　allocation　strategy　in　multiple　unmanned　aerial　vehicles　(UAVs)-assisted　edge　computing　system　with　nonlinear　energy　harvesting　is　investigated　in　this　paper.　The　cooperation　between　BS　and　multi-UAV　is　considered,　which　can　provide　extensive　coverage　for　users　with　mobility.　Mobile　users　can　simultaneously　offload　computation　bits　to　the　BS　and　the　UAV,　and　mobile　users　harvest　energy　from　BS　and　UAV.　Meanwhile,　the　mobility　of　users　is　taken　into　account.　Moreover,　an　echo　state　network　(ESN)-based　prediction　algorithm　is　utilized　for　predicting　the　future　positions　of　mobile　users.　Therefore,　the　UAV　can　reach　the　predicted　users＇　positions　in　advance　to　ensure　the　continuity　of　communication.　The　objective　of　the　resource　allocation　strategy　is　to　maximize　the　energy　efficiency　by　jointly　optimizing　bandwidth　allocation,　computation　resources,　the　trajectory　of　UAV,　and　transmitting　power　of　mobile　users.　Then,　the　resource　allocation　problem　is　formulated　as　a　mixed-integer　nonlinear　programming　problem.　The　quantum-behaved　particle　swarm　optimization　(QPSO)　algorithm　is　used　to　solve　the　problem.　Simulation　results　demonstrate　that　the　proposed　strategy　can　achieve　higher　energy　efficiency　than　other　benchmark　strategies.　In　addition,　QPSO　algorithm　outperforms　the　standard　particle　swarm　optimization　algorithm　and　genetic　algorithm　in　terms　of　energy efficiency.　©　2023　The　Authors.　IET　Communications　published　by　John　Wiley　&　Sons　Ltd　on　behalf　of　The　Institution　of　Engineering　and　Technology.