Modelling of Dynamical Systems

The course will cover the basics of modeling of both physical systems (in the form of ordinary and partial differential equations), computing and scheduling systems (as finite state machines), and combinations thereof (as hybrid models).

Physical systems modeling. The course will cover the basics of Lagrangian modelling, I.e. employing energy balances and the Euler-Lagrange equations to arrive to closed form state-space dynamical equations for system analysis and control design. Bond-graph modelling will be covered as a powerful tool for modelling engineering systems, especially when different physical domains are involved. The use of ordinary and of partial differential equations will be presented extensively as a tool to obtain first principles models. The basic ideas of model reduction, a technique to reduce the complexity of dynamical models, may also be covered in the course. The fundamental differences and connections between continuous vs discrete time modelling will be discussed.

Finite State Models. An introduction to models traditionally employed for computation, e.g. finite state machines, automata, and petri-nets, will be provided. Particular attention will be given to the applicability of these models to provide high-level dynamic descriptions of discrete-event systems and for behaviour specifications of designs.

Hybrid systems. The course will finalize with an introduction to hybrid systems through the formalisms of: Hybrid automata and jump-flow systems, and presenting a brief number of interesting subclasses of hybrid systems, e.g. PWA systems, and timed-automata.