Set-based computing methods are the foundation of validated arithmetics, reliable computing, uncertainty propagation, computational configuration analysis, optimization of control invariant sets, robust control, hybrid system analysis, safe learning and dual control, multi-objective optimization, ambiguity analysis, and many others. Therefore, the first part of this talk is about recent breakthroughs in the field of set-based computing. In detail, we focus on a novel class of configuration-constrained polytopes that admit a joint affine parameterization of their vertices and facets. This parameterization can be used to optimize the location and geometric shapes of potentially high dimensional polytopes with millions of facets and vertices by relying on a large-scale linear program (LP) solver. And the second part of this talk discusses applications of such configuration-constrained polytopes in the context of robust model predictive control, set-theoretic dissipativity theory, information-theoretic safe learning, as well as polytopic dual control. The talk concludes with a general assessment of the state of the art in set-based computing and highlights important avenues for future research.
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