Safe polyhedral tubes for locally convexified MPC

The note considers optimal and model predictive controls for linear systems with strictly convex quadratic stage and terminal cost functions, and under closed polyhedral stage constraints, finitely many open spherical exclusion stage constraints, and closed polyhedral terminal constraints. The computational complexity of exact nonconvex optimal and model predictive controls is alleviated through the local convexification of the nonconvex exclusion constraints, which is obtained via safe polyhedral tubes. The safe polyhedral tubes are constructed via simple algebraic operations and are of paramount importance for the design of locally convexified optimal and model predictive controls via strictly convex quadratic programming.