Low complexity suboptimal explicit NMPC

We present a method for calculating suboptimal explicit solutions to NMPC problems that guarantee stable closed-loop behavior. These explicit solutions are piecewise affine functions that are defined on a polytopic partition of the state space. In contrast to other approaches, we do not only calculate an inner approximation, but also an outer approximation, of the closed-loop stable set. The approximation gap can be used to control the resolution of the state space partition. The proposed approach is illustrated with an example. Despite the simplicity of the example, the results show that the combination of a piecewise affine function and a polytopic partition results in an explicit control law of significantly lower complexity than those from previous approaches.