The　recent　advancements　of　mobile　edge　computing　(MEC)　technologies　and　unmanned　aerial　vehicles　(UAVs)　have　provided　resilient　and　flexible　computation　services　for　ground　users　beyond　the　coverage　of　terrestrial　service.　In　this　paper,　we　focus　on　a　UAV-assisted　MEC　system　in　which　the　UAV　equipped　with　MEC　servers　is　used　to　assist　user　devices　in　computing　their　tasks.　To　minimize　the　weighted　average　energy　consumption　and　delay　in　the　UAV-assisted　MEC　system,　a　LQR-Lagrange-based　DDPG　(LLDDPG)　algorithm,　which　jointly　optimizes　the　user　task　offloading　and　the　UAV　trajectory　design,　is　proposed.　To　be　specific,　the　LLDDPG　algorithm　consists　of　three　subproblems.　The　DDPG　algorithm　is　used　to　address　the　issue　of　UAV　desired　trajectory　planning,　and　subsequently,　the　LQR-based　algorithm　is　employed　to　achieve　the　real-time　tracking　control　of　UAV　desired　trajectory.　Finally,　the　Lagrange　duality　method　is　proposed　to　solve　the　optimization　problem　of　computational　resource　allocation.　Simulation　results　indicate　that　the　proposed　LLDDPG　algorithm　can　effectively　improve　the　system　resource　management　and　realize　the　real-time　UAV　trajectory　design.