  We propose adaptation strategies to modify the standard constrained model
predictive controller scheme in order to guarantee a certain lower bound on the
degree of suboptimality. Within this analysis, the length of the optimization
horizon is the parameter we wish to adapt. We develop and prove several
shortening and prolongation strategies which also allow for an effective
implementation. Moreover, extensions of stability results and suboptimality
estimates to model predictive controllers with varying optimization horizon are
shown.
