Handling the Constraints in Min-Max MPC

Abstract

One of the major sources of conservativeness in min-max model predictive control (MPC) is the handling of constraints, where the ellipsoidal robust invariant set is utilized for the proposal of sufficient and conservative conditions for the satisfaction of the constraints. In this article, in order to reduce the conservativeness due to the constraint handling, we add additional relaxation variables to the physical constraints and propose a two-step approach through relaxing the constraints by the amount which is determined by the calculating of the maximal admissible set (MAS). The constraints are relaxed in an iterative manner to avoid the constraints violation, and the constraint relaxation variables are degrees of freedom for relaxing the constraints and improving the control performance. Moreover, we show that under certain circumstance, the physical constraints can be removed without the constraint violation. The proposed approach is shown to be recursively feasibility and its effectiveness is verified through an air conditioning control in a building energy system. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Buildings are account for large percentage of worldwide energy consumptions. One of the most applicable method for optimization of building energy system subject to multiple constraints is the model predictive control (MPC). However, the industrial MPC is usually not recursively feasible, which implies that the optimization problem can become infeasible and the software will be terminated at some time. In order to apply the MPC synthesis approach (MPC with recursive feasibility guarantee), we have to overcome the conservativeness problem due to the handling of constraints. We propose a useful approach in this work by introducing relaxation variables which act as degrees of freedom for improving the control performance, while the physical constraints are still satisfied. The proposed approach is verified through an example of a 24m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^2$</tex-math> </inline-formula> office room located in Cyber-Physical Energy System (CPES) lab in Western China Science and Technology Innovation Harbour in Xianyang, China. The numerical results show the performance improve of the proposed approach.