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.