Model predictive control with generalized input parametrization

In this article it is investigated how, alternative to e.g. the standard pulse or blocking mechanisms, other input parametrizations can be used in model predictive control to improve the trade-off between performance and complexity. An efficient parametrization is obtained using the observation that the class of all solutions to a finite or infinite horizon LQ control problem can be parametrized with a number of free parameters that is equal to the model order, without loss of performance. The infinite horizon controller with this parametrization is shown to provide a stable closed-loop system, also if constraints are active. The complexity of the parametrization can be systematically reduced using standard reduction techniques, such as e.g. LQG-balanced reduction, which provide an indication of the performance loss. Constrained stability of the closed-loop system is preserved with this reduction approach. The proposed algorithms are illustrated with simulation examples.