Explicit MPC of LPV systems in the controllable canonical form

We exploit the controllable canonical form of single-input linear parameter-varying (LPV) systems to synthesize explicit Model Predictive Control (MPC) feedback laws. The nonlinear state-parameter dependence is first moved into the feedback term, followed by devising a suitable input constraint set. This allows the MPC problem to be formulated with a quadratic performance index, avoiding costly dynamic programming iterations. The resulting MPC optimization is shown to be convex and can be solved parametrically. The explicit solution takes a form of a piecewise affine (PWA) function which allows to implement the feedback law quickly even with limited computational resources.