# System Structure Evolution, Systems Redesign and Control: The Case of Passive Electrical Networks

The problem of redesigning systems by changing elements, topology, organization is a major challenge where systems and control theory have a major role to play. Network redesign is a process involving an evolution to system structure under different types of transformations. A special case is the redesign of passive electric networks which aims to change the natural dynamics of the network (natural frequencies) by modification of the network. As such, this is a problem that it is different to a standard control problem since it involves changing the values of the elements and possibly the topology of the network to achieve the desirable natural frequencies. In fact this problem involves the selection of alternative values for dynamic elements (inductances, capacitances) and non-dynamic (resistances) elements within a fixed interconnection topology and/or alteration of the interconnection topology and possible evolution of the network (increase of elements, branches). We use impedance and admittance modelling for electrical passive networks which are described by integral differential symmetric linear operators and this introduces a new form of *implicit description*. In our study we identify two natural topologies expressing the structured transformations which are identified as the impedance graph- and the admittance graph-topology of the network. Integral part of the study is the mathematical characterization and the representation of the different types of transformations that may be applied on the structured network models. Such transformations are characterized and an appropriate representation is introduced which in turn provides an appropriate set up for the study of the natural frequencies. Within this structured framework we consider characterization of the McMillan degree of the implicit description and the effect of changes of dynamic, or non-dynamic element on the natural frequencies. A general control theoretic framework for addressing issues of systems redesign is presented using Control Theory.

Short biograf of Prof. Karcanias**Nicos Karcanias** is Professor of Control Theory and Design, and he is the Director of the Systems and Control Centre and has been as Associate Dean for Research for the School of Engineering and Mathematical Sciences (2001-2014). His expertise and interests are in the areas of Control Theory, General Systems Theory, Modelling of Complex Systems and Applied Mathematics . He is Fellow of IET (IEE), Fellow of IMA and Life Senior Member of IEEE. He is a member of EPSRC College since its establishment, member of many EU panels on research, Editor of IMA Journal of Mathematical Control and Information, Associate Editor for IEEE Conferences and serves on the Editorial Board of a number of Journals and Conferences. He has made contributions in the areas of Systems, Control Theory, Mathematical Methods, and Computations where novel approaches have been introduced. His research on the Control fundamentals has been accompanied by an effort to migrate Systems and Control to Complex problems, such as the development of a Control based methodology for *Systems Integration*, and the use of Control concepts and techniques for understanding issues in *Complex Systems.* Current research is focused on the study of the notion of *System of Systems *and the development of the general theory for *Structure Evolving Systems* emerging in Systems Integration and Life-Cycle design problems. He is the author/coauthor of over 260 papers published in Scientific Journals and Conference Proceedings and has supervised 34 completed PhD thesis. His research has been supported by a number of EU projects and EPSRC.