Giovanni Granato

Level-Set Approach for Reachability Analysis of Hybrid Systems under Lag Constraints

This study aims at characterizing a reachable set of a hybrid dynamical system with a lag constraint in the switch control. The setting does not consider any controllability assumptions and uses a level-set approach. The approach consists of the introduction of an adequate hybrid optimal control problem with lag constraints on the switch control whose value function allows a characterization of the reachable set. The value function is in turn characterized by a system of quasi-variational inequalities (SQVI). We prove a comparison principle for the SQVI which shows uniqueness of its solution. A class of numerical finite difference scheme for solving the system of inequalities is proposed, and the convergence of the numerical solution toward the value function is studied using the comparison principle. Some numerical examples illustrating the method are presented. Our study is motivated by an industrial application. We are interested in the maximum range of hybrid vehicles.

A stochastic dynamic principle for hybrid systems with execution delay and decision lags

This work presents a stochastic dynamic programming (SDP) algorithm that aims at minimizing an economic criteria based on the total energy consumption of a range extender electric vehicle (REEV). This algorithm integrates information from the REEVs navigation system in order to obtain some information about future expected vehicle speed. The model of the vehicles energetic system, which consists of a high-voltage (HV) battery, the main energy source, and an internal combustion engine (ICE), working as an auxiliary energy source), is written as a hybrid dynamical system and the associated optimization problem in the hybrid optimal control framework. The hybrid optimal control problem includes two important physical constraints on the ICE, namely, an activation delay and a decision lag. Three methods for the inclusion of such physical constraints are studied. After introducing the SDP algorithm formulation we comment on numerical results of the stochastic algorithm and its deterministic counterpart.