Null controllable sets of unstable systems and their application to MPC

Model Predictive Control (MPC) is a popular advanced control strategy that is implemented by determining an optimal control sequence at each time step. One of the major contributors to MPC's computational complexity is the length of the control sequence or, equivalently, the number of optimisation parameters. This paper analyses the null controllable sets, and their related finite horizon approximation, of a class of unstable systems. The analysis reveals that the same control action can be obtained using a much smaller set of control moves via a technique which we term reduced parameterisation.