Geometric control of hybrid systems

In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched linear systems. We reformulate the invariance of a set as an inequality for its support function that is valid for any convex set. This produces novel algebraic conditions for the invariance of sets with polynomial or piecewise quadratic support functions.     

Asymmetric C1 Extension of Aldehydes through Biocatalytic Cascades for Stereodivergent Synthesis of Mandelic Acids

The development of mild, efficient, and enantioselective methods for preparing chiral building blocks from simple, renewable carbon units has been a long-term goal of the sustainable chemical industry. Mandelate derivatives are valuable pharmaceutical intermediates and chiral resolving agents, but their manufacture relies heavily on highly toxic cyanide. Herein, we report (S)-4-hydroxymandelate synthase (HmaS)-centered biocatalytic cascades for the synthesis of mandelates from benzaldehydes and glycine. We show that HmaS can be engineered to perform R-selective hydroxylation by single-point mutation, empowering the stereodivergent synthesis of both (S)- and (R)-mandelate derivatives. These biocatalytic cascades enabled the production of various mandelate derivatives with high atom economy as well as excellent yields (up to 98 %) and ee values (up to >99 %). This methodology offers an effective cyanide-free technology for greener and sustainable production of mandelate derivatives.