Linear MPC with time-varying terminal cost using sparse convex combinations and bisection search

In recent years, different constrained MPC-schemes using a time-varying terminal cost have been introduced. These schemes allow for a natural trade-off to be made between feasibility and optimality at each time step. Their main disadvantage, however, is the increase in on-line computational complexity, compared to MPC (model predictive control) with fixed terminal cost. The main focus of this paper is the introduction of a new method that allows for a significant part of the computation to be done off-line, leading to an improved on-line computational complexity. This is achieved by calculating a set of terminal controllers, terminal costs and terminal constraints off-line. A time-varying terminal cost is then obtained by on-line making convex combinations based on these ingredients. A further improvement is achieved by considering, at each time step, only a relevant subset of the entire set of costs and constraints, without sacrificing stability or control performance. An on-line bisection search algorithm is used to select this subset.