{"ID":2846161,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.02433","arxiv_id":"2511.02433","title":"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.","short_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 co...","url_abs":"https://arxiv.org/abs/2511.02433","url_pdf":"https://arxiv.org/pdf/2511.02433v1","authors":"[\"Stefan S. Mihai\",\"Florin Stoican\",\"Martin Monnigmann\",\"Bogdan D. Ciubotaru\"]","published":"2025-11-04T10:06:52Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}