Feasible mode enumeration and cost comparison for explicit quadratic model predictive control of hybrid systems

For hybrid systems in piecewise affine (PWA) form, this paper presents a new methodology for computing the solution, defined over a set of (possibly overlapping) polyhedra, of the finite-time constrained optimal control problem based on quadratic costs. First, feasible mode sequences are determined via backward reachability analysis, and multiparametric quadratic programming is employed to determine candidate polyhedral regions of the solution and the corresponding value functions and optimal control gains. Then, the value functions associated with overlapping regions are compared in order to discard those regions whose associated control law is never optimal. The comparison problem is, in general, nonconvex and is tackled here as a DC (Difference of Convex functions) programming problem