This thesis investigates optimization-based control allocation methods designed for fault-tolerant and scalable application in multi-stage rockets. It is particularly focused on rockets with Thrust Vector Control (TVC), aerodynamic fins and Reaction Control Systems (RCS). The aim is to minimize the error between control commands and actuator output, besides actuator effort. Both in nominal and faulty conditions. Three convex optimization formulations are proposed: an Angle-Deflection (AD) problem, a linearized problem and a Second-Order Cone Programming (SOCP) problem. The AD problem includes actuator deflections and the linearized and SOCP formulations jointly consider actuator deflections and engine throttling. This work allows integration of faulty scenarios by constraint tightening, allowing reconfiguration of control allocation without changing the problem structure. Simulation data is used to validate the effectiveness of the formulations in satisfying control commands and fault handling. The work contributes to fault-tolerant and scalable control allocation frameworks.