Construction of parametric barrier functions for dynamical systems using interval analysis

International audienceRecently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe subset in which the state can be proved to remain and the complementary subset containing some unsafe region. This approach does not require any reachability analysis, but needs the computation of a valid barrier function, which is difficult when considering general nonlinear systems and barriers. This paper presents a new approach for the construction of barrier functions for nonlinear dynamical systems. The proposed technique searches for the parameters of a parametric barrier function using interval analysis. Complex dynamics can be considered without needing any relaxation of the constraints to be satisfied by the barrier function

Contracts as specifications for dynamical systems in driving variable form

This paper introduces assume/guarantee contracts on continuous-time control systems, hereby extending contract theories for discrete systems to certain new model classes and specifications. Contracts are regarded as formal characterizations of control specifications, providing an alternative to specifications in terms of dissipativity properties or set-invariance. The framework has the potential to capture a richer class of specifications more suitable for complex engineering systems. The proposed contracts are supported by results that enable the verification of contract implementation and the comparison of contracts. These results are illustrated by an example of a vehicle following system.Comment: 8 pages, 2 figures; minor changes in the final version, as accepted for publication in the Proceedings of the 2019 European Control Conference, Naples, Ital

Modular Analysis of Distributed Hybrid Systems using Post-Regions (Full Version)

We introduce a new approach to analyze distributed hybrid systems by a generalization of rely-guarantee reasoning. First, we give a system for deductive verification of class invariants and method contracts in object-oriented distributed hybrid systems. In a hybrid setting, the object invariant must not only be the post-condition of a method, but also has to hold in the post-region of a method. The post-region describes all reachable states after method termination before another process is guaranteed to run. The system naturally generalizes rely-guarantee reasoning of discrete object-oriented languages to hybrid systems and carries over its modularity to hybrid systems: Only one dL-proof obligation is generated per method. The post-region can be approximated using lightweight analyses and we give a general notion of soundness for such analyses. Post-region based verification is implemented for the Hybrid Active Object language HABS