This paper describes the principles of a decentralized framework for the guaranteed collision avoidance of Multi-Agent dynamical systems sharing a common working space. The results are constructive and can be effective in the certification of mission safety. The geometric aspects of the collision avoidance problem are exploited to define the control policies. The main contributions are related to the optimization-based decentralized feedback control which renders a so-called functioning zone controlled invariant. An illustrative example is analyzed in order to highlight the effectiveness of the proposed approaches.