LAUSR

System analysis and control for systems described by partial differential equations (PDEs) is undoubtedly a challenging research area and a lot of progress has been achieved recently. Nevertheless, compared to the methods that are available in the case of ordinary differential equations (ODEs) (including the nonlinear case), the situation in the PDE case is muchmore delicate and a lot of open questions still need to be attacked. Based on an appropriate mathematical model, the so-called late lumping approach is the favourable method in the PDE scenario, as the controller is directly designed on the basis of the distributed-parameter model and the control law is then (numerically) approximated for the purpose of implementation on the real system.Methods like backstepping, flatness-based techniques and energybased approaches have successfully been realized in this late lumping setting. From a physical point of view, the energy-based approaches play an important role as it is possible to consider a sub-class of infinite-dimensional systems, such that the structure of the equations may be linked to the underlying physical principles. From the ODE case it is well-known that port-Hamiltonian systems possess this pleasing property (especially when the Hamiltonian corresponds to energy); therefore, it is reasonable to follow this guide also in the PDE scenario, where (besides others) an additional challenge, the possibility of non-zero energy flow over the boundary, arises – a scenario that has no counterpart in the finite-dimensional case. From an interconnection and control viewpoint, such a treatment of boundary conditions is essential for the incorporation of energy exchange through the boundary, since in many applications, the interconnection with the environment takes place precisely through the boundary. Transferring this concept of the port-Hamiltonian picture from the finitedimensional case to the infinite-dimensional case is not unique, but interesting is the observation that geometric structures are the guide in most of the approaches. This special issue is concerned with modelling aspects of PDEs, with the port-Hamiltonian representation and with the energy based control of distributed-parameter systems. The papers are based on selected contributions that were presented in a special session of the 8th MATHMOD conference in February 2015, Vienna, Austria. The first contribution ‘Distributed port Hamiltonian modeling for irreversible processes’ by W. Zhou, B. Hamroun, F. Couenne and Y. Le Gorrec is discussing the transmission line and a nonisothermal reaction diffusion process in a port-Hamiltonian setting using a Stokes-Dirac structure with the focus on the irreversible (thermo)dynamic system behaviour. The authors show that the first and the second thermodynamic principles can be naturally derived from the proposed representation. The second paper by L. Jadachowski, A. Steinböck and A. Kugi with the title ‘Twodimensional thermal modeling with specular reflections in an experimental annealing furnace’ is dealing with the distributed parameter modelling of the temperature in an experimental annealing device. A finite difference approximation of the governing PDEs is given, and the validation of the model is carried out by comparison with measurements from the considered experimental annealing furnace. The contribution by Y. Vetyukov, E. Oborin, M. Krommer and V. Eliseev with the title ‘Transient modeling of flexible belt drive dynamics using the equations of a deformable string with discontinuities’ is studying the mathematical modelling for the transient analysis of the dynamics of a belt drive. A numerical scheme for solving the underlying PDEs is discussed. The model captures the effects of discontinuous velocity fields and concentrated contact forces. The first three papers are dealing with modelling aspects of infinite-dimensional systems, whereas the following two contributions are discussing control concepts in the PDE scenario. The paper ‘Distributed and backstepping boundary controls for port Hamiltonian systems with symmetries’ by