Explicit MPC for the constrained zonotope case with low-rank matrix updates

Abstract

Solving the explicit Model Predictive Control (MPC) problem requires enumerating all critical regions and their associated feedback laws, a task that scales exponentially with the system dimension and the prediction horizon, as well. When the problem's constraints are boxes or zonotopes, the feasible domain admits a compact constrained-zonotope representation. Building on this insight, we exploit the geometric properties of the equivalent constrained-zonotope reformulation to accelerate the computation of the explicit solution. Specifically, we formulate the multi-parametric problem in the lifted generator space and solve it using second-order optimality conditions, employ low-rank matrix updates to reduce computation time, and introduce an analytic enumeration of candidate active sets that yields the explicit solution in tree form.