The purpose of the this work is to apply optimal control techniques to enhance the performance of the power management of hybrid vehicles. More precisely, the techniques concerned are viscosity solutions of Hamilton-Jacobi equations, level set methods in reachability analysis, stochastic dynamic programming, stochastic dual dynamic programming and chance constrained optimal control. This document starts by presenting the necessary technical background and models for the study of optimal power management of hybrid vehicles. The synthesis of efficient power management strategies for hybrid vehicles accounting for uncertainty in the vehicle speed is studied next. This is done via a stochastic dynamic algorithm, at a first time, and then by a stochastic dual dynamic programming algorithm. In addition, we introduce a chance constrained optimal control problem that can be used to synthesize more flexible optimal control strategies. We detail a dynamic programming principle in a form that can be readily used for the numerical synthesis of optimal feedback using a dynamic programming algorithm. Later, theoretical results regarding the reachability analysis of hybrid systems are obtained. The reachability set of a continuous-time hybrid system is characterized by a value function via a level set approach. Furthermore, we show that the value function of a hybrid optimal control problem is the unique solution of a system of quasi-variational inequalities in the viscosity sense. Then, we prove the convergence of a class of numerical schemes for the computation of the value function. As a further step in the reachability analysis, we study of the discrete-time dynamical system and the discrete-time optimal control problem for the reachability analysis of hybrid systems. Here, the focus is on a discrete-time modeling of the hybrid system, which leads to dynamic programming principle, which can be used to characterize the value function. Lastly, we describe the construction of a stochastic model of the speed profile for electric vehicles.
