## Final Activity Report Summary - PARAMCOSYS (Parametrisation in the control of dynamic systems)

The main goal in the project was to study parametrisation of dynamic systems. These systems are controlled ordinary and partial differential equations and systems of equations. Parametrisation means that the input, or control, and output, or measurement, of the system considered are calculated by using a third signal function, so-called parameter function. Then, the system equations need not be directly solved to obtain the corresponding input-output pairs of the system.

The approach used is a generalisation of so-called flatness-based control design applicable directly only to ordinary differential system models. A generalisation of the differential equation models, so-called pseudo-differential operator models, was considered, too. In a series of published conference papers parametrisation of two scalar boundary-controlled distributed-parameter systems were studied. These are the linear heat equation and a nonlinear viscous Burgers' equation, which are described by partial differential equation models. A general treatment on parametrisation of a set of linear partial differential equation systems was carried out in a more detailed paper.

Our main application field on the side of ordinary differential equation models is quantum control, in other words, quantum-mechanically described systems and their control. These system classes are studied by using bilinear control models. Then we could use a certain type of exponential representation of the solution of the model equations, so-called Wei-Norman solution in the construction of the parametrisation. Simulation studies of our solution methodology are under work. Development and analysis of some more realistic and sophisticated quantum system models are going on, too.

The approach used is a generalisation of so-called flatness-based control design applicable directly only to ordinary differential system models. A generalisation of the differential equation models, so-called pseudo-differential operator models, was considered, too. In a series of published conference papers parametrisation of two scalar boundary-controlled distributed-parameter systems were studied. These are the linear heat equation and a nonlinear viscous Burgers' equation, which are described by partial differential equation models. A general treatment on parametrisation of a set of linear partial differential equation systems was carried out in a more detailed paper.

Our main application field on the side of ordinary differential equation models is quantum control, in other words, quantum-mechanically described systems and their control. These system classes are studied by using bilinear control models. Then we could use a certain type of exponential representation of the solution of the model equations, so-called Wei-Norman solution in the construction of the parametrisation. Simulation studies of our solution methodology are under work. Development and analysis of some more realistic and sophisticated quantum system models are going on, too.