  This paper presents a heterogeneously parameterized tube-based model
predictive control (MPC) design applicable to linear parameter-varying (LPV)
systems. In a heterogeneous tube, the parameterizations of the tube cross
sections and the associated control laws are allowed to vary along the
prediction horizon. Two extreme cases that can be described in this framework
are scenario MPC (high complexity, larger domain of attraction) and homothetic
tube MPC with a simple time-invariant control parameterization (low complexity,
smaller domain of attraction). In the proposed framework, these extreme
parameterizations, as well as other parameterizations of intermediate
complexity, can be combined within a single tube. By allowing for more
flexibility in the parameterization design, one can influence the trade-off
between computational cost and the size of the domain of attraction. Sufficient
conditions on the parameterization structure are developed under which
recursive feasibility and closed-loop stability are guaranteed. A specific
parameterization that combines the principles of scenario and homothetic tube
MPC is proposed and it is shown to satisfy the required conditions. The
properties of the approach, including its capability of achieving improved
complexity/performance trade-offs, are demonstrated using two numerical
examples.
