  Complex real-world applications of cyber-physical systems give rise to the
need for multi-objective controller synthesis, which concerns the problem of
computing an optimal controller subject to multiple (possibly conflicting)
criteria. The relative importance of objectives is often specified by human
decision-makers. However, there is inherent uncertainty in human preferences
(e.g., due to artifacts resulting from different preference elicitation
methods). In this paper, we formalize the notion of uncertain human preferences
and present a novel approach that accounts for this uncertainty in the context
of multi-objective controller synthesis for Markov decision processes (MDPs).
Our approach is based on mixed-integer linear programming and synthesizes an
optimally permissive multi-strategy that satisfies uncertain human preferences
with respect to a multi-objective property. Experimental results on a range of
large case studies show that the proposed approach is feasible and scalable
across varying MDP model sizes and uncertainty levels of human preferences.
Evaluation via an online user study also demonstrates the quality and benefits
of the synthesized controllers.
