Group and total dissipativity and stability of multi-equilibria hybrid automata

Complex systems, which consist of different interdependent and interlocking subsystems, typically have multiple equilibrium points associated with different set points of each operation mode. These systems are usually interpreted as switched systems, or in general, as hybrid systems. Surprisingly, the consideration of multiple equilibria is not common in hybrid systems’ literature, being typically focused on the study of stability and dissipativity properties for switched systems whose subsystems share the same equilibrium point. This paper will expand the discussion to the case of having multiple co-existing equilibrium points for hybrid systems modelled as hybrid automata, which are more general than switched systems. A classification of equilibria for hybrid automata is offered, and some stability related properties are shown for them. Moreover, some dissipativity-related properties are studied. The chief idea of our approach is to identify stable and dissipative components as group of discrete locations within the hybrid automaton. Two examples are used to illustrate our conclusions

A novel hybrid automaton framework for multi-phase epidemic modelling

This is an accepted manuscript of an article published by IEEE on behalf of SCS on 05/10/2021 The accepted version of the publication may differ from the final published version.A framework for the multi-phase epidemic modelling of SEIARD (Susceptible-Exposed-symptomatic Infectious-Asymptomatic infectious-Recovered by immunity or by vaccination-Dead due to the disease) subpopulations is produced with switching transmission rate, basic reproduction ratio and vaccination strategy. Thekey novel featureof our modelis that we reproduce the different phasesof theevolutionof the infectious diseasebyusingahybrid automatonwithdifferent discrete locations correspondingtoeachof the phases of the disease. This is a general modelling framework applicable to the spreading of infectious diseases.We showhow the proposed modelworks with the simulationof different scenarios

Approximated stability analysis of bi-modal hybrid co-simulation scenarios

This is an accepted manuscript of an article published by Springer in: Cerone A., Roveri M. (eds) Software Engineering and Formal Methods. SEFM 2017. Lecture Notes in Computer Science, vol 10729, available online at: https://doi.org/10.1007/978-3-319-74781-1_24 The accepted version of the publication may differ from the final published version. For information on re-use, please refer to the publisher’s terms and conditions.Co-simulation is a technique to orchestrate multiple simulators in order to approximate the behavior of a coupled system as a whole. Simulators execute in a lockstep fashion, each exchanging inputs and output data points with the other simulators at pre-accorded times. In the context of systems with a physical and a cyber part, the communication frequency with which the simulators of each part communicate can have a negative impact in the accuracy of the global simulation results. In fact, the computed behavior can be qualitatively different, compared to the actual behavior of the original system, laying waste to potentially many hours of computation. It is therefore important to develop methods that answer whether a given communication frequency guarantees trustworthy co-simulation results. In this paper, we take a small step in that direction. We develop a technique to approximate the lowest frequency for which a particular set of simulation tools can exchange values in a co-simulation and obtain results that can be trusted.Published versio

Deadness and how to disprove liveness in hybrid dynamical systems

© 2016 The Authors. Published by Elsevier. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1016/j.tcs.2016.06.009What if we designed a tool to automatically prove the dynamical properties of systems for which analytic proof is difficult or impossible to obtain? Such a tool would represent a significant advance in the understanding of complex dynamical systems with nonlinearities. This is precisely what this paper offers: a solution to the problem of automatically proving some dynamic stability properties of complex systems with multiple discontinuities and modes of operation modelled as hybrid dynamical systems. For this purpose, we propose a reinterpretation of some stability properties from a computational viewpoint, chiefly by using the computer science concepts of safety and liveness. However, these concepts need to be redefined within the framework of hybrid dynamical systems. In computer science terms, here, we consider the problem of automatically disproving the liveness properties of nonlinear hybrid dynamical systems. For this purpose, we define a new property, which we call deadness. This is a dynamically-aware property of a hybrid system which, if true, disproves the liveness property by means of a finite execution. We formally define this property, and give an algorithm which can derive deadness properties automatically for a type of liveness property called inevitability. We show how this algorithm works for three different examples that represent three classes of hybrid systems with complex behaviours.This work has been supported by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under the framework of the project DYVERSE: A New Kind of Control for Hybrid Systems (EP/I001689/1). The first author also acknowledges the support of the Research Councils UK under the grant EP/E50048/1.Published versio