  We consider nonlinear model predictive control (MPC) with multiple competing
cost functions. In each step of the scheme, a multiobjective optimal control
problem with a nonlinear system and terminal conditions is solved. We propose
an algorithm and give performance guarantees for the resulting MPC closed loop
system. Thereby, we significantly simplify the assumptions made in the
literature so far by assuming strict dissipativity and the existence of a
compatible terminal cost for one of the competing objective functions only. We
give conditions which ensure asymptotic stability of the closed loop and, what
is more, obtain performance estimates for all cost criteria. Numerical
simulations on various instances illustrate our findings. The proposed
algorithm requires the selection of an efficient solution in each iteration,
thus we examine several selection rules and their impact on the results.
