Dissipativity-related properties in hybrid automata

This research explores energy-related properties of hybrid systems, especially in hybrid automata. Here, energy refers to the abstract energy of the system which may not have a physical interpretation. The formalization of the abstract energy of dynamical systems is achieved by means of the dissipativity theory, which analyses dynamical systems behaviour by means of the exchange of energy with the environment. A dissipative system does not generate and cannot store all the energy supplied to it. Instead, it dissipates energy in some way. Different classes of dissipativity can be obtained according to the balance between the stored and the externally supplied energy in a system. The most important among these is passivity. Dissipativity, especially passivity, has been extensively used in feedback control because of its stability implications. However, they have been overlooked in the analysis and control of hybrid systems, and have been especially underused in the computational-oriented modelling framework of hybrid automata.

This research fills the gap between dissipativity theory and hybrid systems. Due to the direct physical interpretation of dissipativity-based analysis and control, the applications of this project are vast and wide-ranging. Depending on the student’s interests, different application domains can be explored. This research would be part of the project DYVERSE (DYnamical-driven VERification of Systems with Energy considerations).