This paper presents a new formulation for provable safety under partial model uncertainty with guaranteed performance. A collision-free control strategy is developed for an uncertain multi-agent system that navigates through a prior unknown environment populated with static and dynamic obstacles. Our novel instantaneous local control barrier functions (IL-CBFs), constructed based on noisy data from limited horizon sensors online, are adopted to characterize potential agent-to-obstacle collisions. These data-based IL-CBFs further serve as the constraints of a quadratic programming (QP) optimization framework to generate safe control inputs. The required model information during the QP optimization process is identified within a finite time by our proposed parameter estimation update law. Numerical simulations based on the reach-avoid game and the formation keeping task are conducted to reveal the effectiveness of the proposed collision-free control strategy.