Power management of NoC-based many-core systems with runtime application mapping becomes more challenging in the dark silicon era. It necessitates a multi-objective control approach to consider an upper limit on total power consumption, dynamic behaviour of workloads, processing elements utilization, per-core power consumption, and load on networkon-chip. In this paper, we propose a multi-objective dynamic power management method that simultaneously considers all of these parameters. Fine-grained voltage and frequency scaling, including near-threshold operation, and per-core power gating are utilized to optimize the performance. In addition, a disturbance rejecter is designed that proactively scales down activity in running applications when a new application commences execution, to prevent sharp power budget violations. Simulations of dynamic workloads and mixed time-critical application profiles show that our method is effective in honoring the power budget while considerably boosting the system throughput and reducing power budget violation, compared to the state-of-the-art power management policies.