The idea of deriving observers for switching networks and using those for deriving distributed controllers still leaves many questions that need to be answered. Roughly the following four stages can be distinguished.
First, observability needs to be properly defined and tests for observability have to be developed. In the above mentioned example both servers are able to reconstruct the state at the other server based on only local information. However, in an acyclic network, information only flows downstream. Therefore, only the “final” server in the network is able to reconstruct the global state information. The “first” server in the network can not reconstruct anything from the global state. A good starting point might be to use a behavioral approach for dynamical systems as presented in ([#References|references]).
Second, observers need to be designed for arbitrary observable networks. As a small deviation in the measurements due to noise should also lead to a small observer error, a general methodology needs to be developed to arrive at observers which reconstruct the global state, but are not too sensitive to noise.
Related to this is also the stability analysis of distributed policies, since the servers are not necessarily synchronized, which is the next issue to address. This will be joint research with prof. Armbruster (Arizona State University, Tempe, AZ; part-time with Systems Engineering Group, Mechanical Engineering, TU/e), including applications to self-organizing networks. For that purpose, the PhD Student should also stay at Arizona State University, Tempe, AZ, for three months, around the end of his/her second year.
Finally, distributed controllers should be designed for networks, which is not simply a combination of state feedback controllers and observers. Notice that even though for an acyclic network the “first” server can not reconstruct anything, the “second” server is able to reconstruct the state at the “first” server and therefore might be able to adjust itself properly to the “first” server. Eventually, the entire network might still converge towards desired network behavior.