DYVERSE: putting together the pieces of the hybrid systems' jigsaw

The automated rendezvous and docking of spacecrafts despite inevitable impacts; the operation of large-scale electrical power networks with renewable generation sources; the automation of public transport scheduling systems in metropolitan areas; the synchronisation of beta-cells in the pancreas; the tracking of people. These are examples of complex systems Their operation is usually safety-critical and requires the maintenance of stability despite uncertainties and the recovery from contingencies minimising losses. Furthermore, they are highly nonlinear, and combine continuous and discrete, smooth and abrupt dynamics. In dynamical systems theory, this is called discontinuous or switching behaviour. Their combined dynamics can be seen as a hybrid dynamical system. DYVERSE is the DYnamical-driven VERification of Systems with Energy considerations. By energy, we refer to abstract energy which may not have a physical interpretation. The formalisation of the abstract energy of dynamical systems is achieved by means of dissipativity theory. But DYVERSE goes beyond the verification of behaviour patterns in discontinuous and switched systems.DYVERSE is a computational-dynamical framework for the modelling, analysis and control of complex control systems under the framework of hybrid systems. But, what is a hybrid system? The term itself is confusing and broad, and can be used for any system consisting of elements of a different nature.DYVERSE framework should be understood as a catalyst of formal computational tools, dynamical systems theory and control engineering methodologies. Can we obtain a discrete abstraction of the different dynamical behaviours of systems for the detection and prevention of harmful dynamics? How can we redefine dynamical properties from a computational viewpoint? How can we integrate these definitions in a feedback control loop to influence the behaviour of systems? There is a long way to walk so that we can answer these questions.