Feasibility for non-square linear MPC

This paper investigates how the attributes of non-square systems affects feasibility in linear (MPC). Following on from the foundation set in [16], which formulated a transparent and simple approach to feasibility in linear MPC, this paper extends these ideas for application to non-square systems. Feasibility is maximised by allowing the dynamic optimisation to choose steady-state states and inputs that give offset-free tracking (as opposed to squaring the system beforehand), and prioritising appropriately between inputs and outputs when set-points are not achievable. A single stage MPC algorithm is presented, linking reference governor approaches, closed-loop paradigm MPC and non-square techniques through an approach that is novel and has the strength of simplicity.