On Monday, July 2, 2018 Dr. Mario Eduardo Villanueva (ShanghaiTech University, China) gave at IAM a lecture on "Backward-forward Reach Set Splitting for Constrained Differential Games".
Title: Backward-forward reach set splitting for constrained differential games Mario E. Authors: Villanueva, Xuhui Feng, Boris Houska
Abstract: In 1960, Rufus Isaacs initiated the investigation of differential game theory. Since then, differential games—which model decision making problems for systems described by differential equations—have found a plethora of application areas, ranging from operations research and economics to control. This talk focuses on the class of two-player zero-sum non-cooperative Stackelberg differential games, under open- and closed-loop control policies. We present a novel formulation of the game in the form of an optimal control problem with set-valued states under the assumption that both players have to satisfy state and control constraints, or, else, loose the game. We discuss differences and similarities to standard robust optimal control problems. Moreover, we outline a numerical solution strategies for analyzing and solving the considered class of differential games designing algorithms that are based on a backward-forward reachable set propagation strategy.