Control allocation is a set of methods for control of modern overactuated mechanical systems (such as aircrafts, marine vehicles, electric cars), and deals with distributing of the total control demand among the individual actuators. The idea of control allocation allows to deal with control constraints and actuator faults separately from the design of the main regulator, which uses virtual control input. Its dimension is usually quite low, while the number of physical actuators can be much higher. Using linearization, control allocation is equivalent to linear inverse problem with interval-constrained vector x, which we need to recover from limited linear measurements: y=Ax. Depending on the particular application, one can seek a sparse solution (which minimizes number of physical actuators used for control) or optimize convex function of x. Note that if x constrained to a hypercube, then y is constrained to its image, a zonotope. We propose a new real-time method for calculating x, which is based on interval analysis ideology. Its basic operations are hypercube bisection and explicit reconstruction of the zonotope as a system of linear inequalities.