This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem of simultaneously minimizing a set of $H_{\infty}$ cost functions for a class of systems subject to bounded disturbances and/or parameter uncertainties. Numeric examples are reported to highlight the stabilizing action of the proposed control laws.