Observer design for linear switched differential-algebraic equations

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A dynamical system comprises a mathematical model of an underlying physical phenomenon.It has two basic components: external signals which interconnects the system with its environment and the internal state that evolves according to the model description. The external signals can usually further be split into inputs and outputs.One of the basic problem associated with any dynamical system is that of constructing an observer which uses the available information of the external signals to estimate the internal state. The purpose of this project is to develop observers for dynamical systems modeled as switched differential-algebraic equations (DAEs). The motivation to study this particular system class is twofold: 1) In contrast to ordinary differential equations (ODEs), DAEs include differential as well as algebraic equations. Practically every system's model also contains algebraic equations in the first place so it is natural to use DAEs (instead of the simplified ODEs) as a starting point. 2) Possible structural changes (like switches in electrical circuits or component faults in general physical system) can be modeled within the framework of switched systems. As an application of the proposed project, consider for example (national) electrical grids, which are large electrical circuits modeled as DAEs. An observer would then be used to monitor the energy flows through the transmission lines and could prevent overloading. Sudden structural changes in electrical grids are common and have to be taken into account; examples are: tripping of power lines due to harsh weather conditions, or a sudden drop in the energy production by wind turbines when whole wind parks are switched off in the presence of too strong winds. Hence a possible application of the theoretical results obtained by the proposed project could be improved monitoring tools for electrical grids.