Reference Tracking MPC using Terminal Set Scaling, Report no. LiTH-ISY-R-3044

A common assumption when proving stability of linear MPC algorithms for tracking applications is to assume that the desired setpoint is located far into the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications this assumption can be severly limiting since the terminal set is relatively large and therefore limits how close the setpoint can be to the boundary of the feasible set. We present simple modifications that can be performed in order to guarantee stability and convergence to setpoints located arbitrarily close to the boundary of the feasible set. The main idea is to introduce a scaling variable which dynamically scales the terminal state constraint set and therefore allows a setpoint to be located arbitrarily close to the boundary. In addition to this the concept of pseudo setpoints are used to gain the maximum possible region of attraction and to handle infeasible references. Recursive feasibility and convergence to the desired setpoint, or its closest feasible alternative, is proven and a motivating example of controlling an agile fighter aircraft is given.