Putting Energy in Control

Arjan van der Schaft

Prevailing trend in the modeling of complex physical systems is modular modeling, where the complex physical system is represented as the network interconnection of ideal components. This has clear advantages in terms of flexibility, re-usability of model parts, and support for automated modeling. On the other hand, the equations of motion obtained from direct network modeling are often complicated and without apparent structure, and will easily contain algebraic constraints arising from the interconnection of the sub-systems. As such, they may not be very suited to analysis and control.

During the last fifteen years it has been shown how a particular type of network modeling, namely port-based modeling , where the sub-systems are interacting with each other through power exchange represented by pairs of conjugated variables, immediately leads to generalized Hamiltonian equations of motion. The resulting class of geometrically defined systems has been called port-Hamiltonian systems. Recently, this framework has been extended to distributed-parameter systems; typical examples including the transmission line, Maxwell's equations, beam models, as well as ideal fluid models. In this presentation we will indicate the potential of this approach for the analysis, simulation and control of complex nonlinear and infinite-dimensional physical systems.