A Parametric Branch and Bound Approach to Suboptimal Explicit Hybrid MPC

In this article we present a parametric branch and bound algorithm for computation of optimal and suboptimal solutions
to parametric mixed-integer quadratic programs and parametric mixed-integer linear programs. The algorithm returns an
optimal or suboptimal parametric solution with the level of suboptimality requested by the user. An interesting application of
the proposed parametric branch and bound procedure is suboptimal explicit MPC for hybrid systems, where the introduced
user-dened suboptimality tolerance reduces the storage requirements and the online computational eort, or even enables
the computation of a suboptimal MPC controller in cases where the computation of the optimal MPC controller would be
intractable. Moreover, stability of the system in closed loop with the suboptimal controller can be guaranteed a priori. Forwarded to publisher