A semi-explicit MPC set-up for constrained piecewise affine systems

Recently quite some effort has been dedicated towards the use of Model Predictive Control (MPC) for regulating discrete-time piecewise affine systems. One of the obstructions for implementation is the high on-line computational load. In this paper we present an approach to reduce the on-line computations by using an algorithm that solves off-line a controllability problem with respect to an invariant target set. The algorithm generates a tree containing minimal discrete events controllable paths to the target set. For an initial state (or a measured state), a controllable path to the target set with a minimal number of discrete events is easily obtained and a resulting ordered sequence of state space regions (sets) is pre-computed; each region corresponds to a single sub-model, part of the piecewise affine system. It is then shown how, under certain assumptions, this controllable path can be used to design a computationally more friendly semi-explicit MPC algorithm for constrained piecewise affine systems. Finally, an example is given for illustration purposes.