A fixed-point implementation of explicit MPC laws

We present a method for the implementation of predictive controllers for linear constrained systems based on fixed-point numbers. Fixed-point implementations are of high practical interest since they are fast and since cheap processing units with low energy consumption are available. Our scheme builds on the assumption that an explicit description of the predictive control law, which is known to be piecewise affine, is at hand. In principle, an implementation of the controller is then straightforward. However, fixed-point representations of the control law and the state measurements cause quantization errors that may affect the stability of the system. We show how robust MPC can be used to compensate those quantization errors and to guarantee robust stability.