An efficient branch and bound algorithm for state estimation and control of hybrid systems

This paper presents a new Branch and Bound tree exploring strategy for solving Mixed Integer Quadratic Programs (MIQP)involving time evolutions of linear hybrid systems. In particular, we refer to the Mixed Logical Dynamical (MLD) models introduced by Bemporad and Morari (1999), where the hybrid system is described by linear equations/inequalities involving continuous and integer variables. For the optimizations required by the controller synthesis and state estimation of MLD systems, the proposed algorithm reduces the average number of node explorations during the search of a global minimum. It also provides good local minima after a short number of steps of the Branch and Bound procedure.