Regional MPC with active set updates

摘要

The solution to a linear MPC problem for a fixed state x is usually interpreted as the optimal feedback signal u(x) for that particular state variable value. The solution to the MPC problem at a point in state space contains more information, however. It does not only determine the optimal feedback signal u(x) at the particular point x, but it determines an affine control law u(·) that provides the optimal feedback on an entire state-space polytope. It is an obvious idea to use this affine control law as long as the closed-loop system stays in the current polytope, and to solve a QP only to determine a new affine law and polytope of validity whenever the current polytope is left. The present paper extends this idea by a method that avoids solving QPs (or optimality conditions) when a new polytope is entered. This is accomplished by triggering active set updates instead of solving QPs or optimality conditions whenever possible. We state conditions under which these active set updates are possible and demonstrate the usefulness of the idea with several examples.