Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints

International audienceThis 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 in the introduction of on 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 differences schemes for solving the system of inequalities is proposed and the convergence of the numerical solution towards 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, namely, that of range extender electric vehicles. This class of electric vehicles uses an additional module -- the range extender -- as an extra source of energy in addition to its main source -- a high voltage battery. The reachability study of this system is used to establish the maximum range of a simple vehicle model

Re-verification of a Lip Synchronization Protocol using Robust Reachability

The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper, we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm. This lip synchronization protocol is an interesting case because timing aspects are crucial for the correctness of the protocol. Several versions of the model are considered: with an ideal video stream, with anchored jitter, and with non-anchored jitter

Re-verification of a Lip Synchronization Algorithm using robust reachability

The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm.This lip synchronization protocol is an interesting case because timing aspect are crucial for the correctness of the protocol. Several versions of the model are considered, with an ideal video stream, with anchored jitter, and with non-anchored jitter

Reachability of Delayed Hybrid Systems Using Level-set Methods

International audienceThis study proposes an algorithm to synthesize controllers for the power management on board hybrid vehicles that allows the vehicle to reach its maximum range along a given route. The algorithm stems from a level-set approach that computes the reachable set of the system, i.e., the collection of states reachable from a certain initial condition via the computation of the value function of an optimal control problem. The discrete-time vehicle model is one of a particular class of hybrid vehicles, namely, range extender electric vehicles (REEV). This kind of hybridization departures from a full electric vehicle that has an additional module -- the range extender (RE) -- as an extra energy source in addition to its main energy source -- a high voltage battery. As an important feature, our model allows for the switching on and off of the range extender and includes a decision lag constraint, i.e., imposes two consecutive switches to be separated by a positive time interval. The approach consists in the introduction of an adequate 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 dynamic programming algorithm. This algorithm is implemented and some numerical examples are presented

Provable Run Time Safety Assurance for a Non-Linear System

Systems that are modeled by non-linear continuous-time differential equations with uncertain parameters have proven to be exceptionally difficult to formally verify. The past few decades have produced a number of useful verification tools which can be applied to such systems but each is applicable to only a subset of possible verification scenarios. The Level Sets Toolbox (LST) is one such tool which is directly applicable to non-linear systems, however, it is limited to systems of relatively small continuous state space dimension. Other tools such as PHAVer and the SpaceEx invariant of the Le Guernic-Girard (LGG) support function algorithm are specifically designed for hybrid systems with linear dynamics and linear constraints but can accommodate hundreds of continuous states. The application of these linear reachability tools to non-linear models has been achieved by approximating non-linear systems as linear hybrid automata (LHA). Unfortunately, the practical applicability and limitations of this approach are not yet well documented. The purpose of this thesis is to evaluate the performance and dimensionality limitations of PHAVer and the LGG support function algorithm when applied to a LHA approximation of a particular non-linear system. A collision avoidance scenario with autonomous differential drive robots is used as a case study to demonstrate that an over-approximated reachable set boundary can be generated and implemented as a run time safety assurance mechanism

Modeling and Analyzing Biomolecular Networks

The authors argue for the need to model and analyze biological networks at molecular and cellular levels. They propose a computational toolbox for biologists. Central to their approach is the paradigm of hybrid models in which discrete events are combined with continuous differential equations to capture switching behavior