Contractive set MPC

Abstract

Model Predictive Control (MPC) is a method much used in the petroleum industries because it can handle multiple states and constraints, and it finds optimal control inputs. The MPC method in this thesis is called contractive set MPC. Contractive set MPC is based on similar principles as the well known dual mode MPC, which consists of a terminal set where the state need to lie inside at the end of the prediction horizon, for constraints to hold on the infinite horizon.Contractive in contractive set MPC refers to the special terminal set being contractive by a certain scalar value, and the basic idea of contractive set MPC is to calculate the terminal set off-line which allows the use of a less time complex on-line controller (linear programming problem) compared to standard MPC methods which also solves an optimization problem repeatedly on-line but instead a quadratic optimization problem is solved repeatedly on-line. The requirements of additional control methods may become apparent if the resulting special terminal set is a very small subset of the state constraint set. Contractive set MPC is therefore enabled for processes which requires fast sampling rates. Another attractive property of the contractive set MPC method is that once the special set has been calculated, more precisely called the supremal (A,B)-invariant lambda-contractive set, closed loop stability easy follows from the properties this set exhibits. Another topic of this thesis is an approximation of the supremal (A,B)-invariant lambda-contractive set, therefore it is not the supremal set any more, but its properties still applies. By using the proposed method in this thesis, an approximation is obtained such that the bad time complexity of the existing recurrence algorithm is avoided, this enables contractive set MPC for processes of high dimension.A review of existing theory is given, and the behaviour of the existing method in the literature is elaborated by two examples in lower dimensions, and the idea to obtain the approximation is sketched at the same time.