Predictive control for hybrid systems. Implications of polyhedral pre-computations

The present paper deals with the predictive control laws for hybrid systems. The modelling formalism used will be the Mixed Logical Dynamical (MLD) which offers the advantage of a compact expression of the dynamics in terms of linear equalities and inequalities on the logical and continuous-time states and inputs. Being an optimization-based control technique, the predictive control needs an efficient implementation scheme in order to be effective in real time.Several studies assess the importance of the prediction horizon and the terminal constraints due to their implications in the structure of the associated optimal control problem. Lately it has been shown that as long as the constraints remain linear, the polyhedral computations can serve as tools for the migration of the on-line computational effort to off-line explicit constructions in terms of explicit solutions which can avoid a costly on-line optimum seeking and thus pushing the application of predictive laws to even higher sampling rates.This paper reviews the on-line optimization techniques proposed for the predictive control of hybrid systems based on mixed integer optimization problems. Further, the explicit solutions are analyzed using a parameterized polyhedron approach.