Polyhedral feasible set computation of MPC-based optimal control problems

Abstract

Feasible sets play an important role in model predictive control &#x0028 MPC &#x0029 optimal control problems &#x0028 OCPs &#x0029. This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron &#x0028 represented by linear matrix inequalities &#x0029 and polyhedral &#x0028 represented by a set of inequalities &#x0029 constraints. According to the geometrical meaning of the inner product of vectors, the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set. After computing the vertices, the convex hull of these vertices is determined which equals the feasible set. The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids the non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.