  In model-predictive control (MPC), achieving the best closed-loop performance
under a given computational resource is the underlying design consideration.
This paper analyzes the MPC design problem with control performance and
required computational resource as competing design objectives. The proposed
multi-objective design of MPC (MOD-MPC) approach extends current methods that
treat control performance and the computational resource separately -- often
with the latter as a fixed constraint -- which requires the implementation
hardware to be known a priori. The proposed approach focuses on the tuning of
structural MPC parameters, namely sampling time and prediction horizon length,
to produce a set of optimal choices available to the practitioner. The posed
design problem is then analyzed to reveal key properties, including smoothness
of the design objectives and parameter bounds, and establish certain validated
guarantees. Founded on these properties, necessary and sufficient conditions
for an effective and efficient solver are presented, leading to a specialized
multi-objective optimizer for the MOD-MPC being proposed. Finally, two
real-world control problems are used to illustrate the results of the design
approach and importance of the developed conditions for an effective solver of
the MOD-MPC problem.
