First we show that continuous piecewise-affine systems are equivalent to max-min-plus-scaling systems (i.e., systems that can be modeled using maximization, minimization, addition and scalar multiplication). Next, we consider model predictive control for these systems. In general, this leads to nonlinear non-convex optimization problems. However, we present a method based on canonical forms for max-min-plus-scaling functions to solve these optimization problems in a more efficient way than by just applying nonlinear optimization as was done in previous research.