Abstract

Hybrid systems provide alternative ways of interpreting and solving many complex engineering systems. Generally speaking, hybrid dynamical systems consist of continuous-type and discrete-event dynamics. They bring together formal computational tools, dynamical systems theory and control engineering methodologies. Consequently, this framework gives rise to models, behaviour analysis tools, stability definitions, control schemes, numerical methods and algorithms for simulation which are novel, and entail a better formulation of the system interaction with the environment.

In this talk, I will present an overview of hybrid systems and the key facts about their modelling, analysis and control. In addition, I will present some of my current research in the abstraction and formal verification of stability properties and complex dynamical behaviours of discontinuous control systems. Discontinuous systems are ubiquitous in engineering applications and are often changeable and unpredictable in behaviour. This has to be taken into account in order to ensure good performance and quality in the control design. I will show several applications in which I have been working.

Can we obtain a discrete abstraction of the different dynamical behaviours of systems for the detection and prevention of harmful dynamics? Is it useful to redefine dynamical properties from a computational viewpoint? How can we integrate the formal verification of these properties in a feedback control loop? There is a long way to go before we can answer these questions satisfactorily.