This paper presents a nonlinear gain-scheduled control design approach using set-valued methods. Previous results for set-valued methods for linear parameter-varying (LPV) systems are applied to nonlinear systems with quasi-LPV representations. The proposed design approach differs from traditional gain-scheduling in several aspects: (1) linearization errors are accommodated as linear state-dependent disturbances, (2) constraints on system states and controls are specified, and (3) rates of transitions among operating regions are explicitly addressed. As a consequence, even "local" set point designs are nonlinear. Nonlinear parameter-dependent state feedback which is guaranteed to achieve constrained regulation, is constructed by solving several linear programs.