Predictive control of hybrid systems under a multi-MLD formalism with state space polyhedral partition

The mixed logical dynamical (MLD) formalism has proved to be an efficient modelling framework for hybrid systems described by dynamics logic and constraints. Furthermore, it allows formulating and solving problems such as control, using for example predictive strategies. However, its main drawback remains the computation load due to the complexity of the mixed integer quadratic programming (MIQP) to be solved. To overcome this problem, this paper presents an innovative technique splitting the global state space to polyhedral subregions, leading to a multi-MLD model. Inside each subregion, a restricted smaller size MLD model can be developed taking into account only variables variations that may occur in this subregion. This approach enables to considerably reduce the computation time, for a more convenient real time implementation with small sampling time. This strategy is applied in simulation to the control of a three tanks benchmark.