Title: Dualities in optimal control theory

Abstract: Duality is a mathematical principle which, when it emerges, signifies the intrinsic relations between two distinct concepts, theorems or structures. In this talk, I will present three dualities which emerge in optimal control theory: (i) the duality in the Minimum Principle (MP) between the finite dimensional spaces of state variations and that of co-state (adjoint) processes, (ii) the duality in Dynamic Programming (DP) between the infinite dimensional space of measures and that of continuous functions, and (iii) the duality in Feynman-Kac theory between partial differential equations (PDEs) and forward-backward stochastic differential equations (FBSDEs). I will present new versions of the MP and DP for deterministic and stochastic hybrid systems and illustrate their implementation and numerical computations for single-agent and multi-agent systems.