Consensus and synchronization problems have been popular subjects in systems and control theory over the last couple of years, mainly motivated by the fact that phenomena summarized under these two terms are observed in various instances in a wide range of scientific disciplines. The two terms both refer to the property that individuals in a group reach agreement in some sense. In addition, couplings are typically of a diffusive type in both cases, i.e., the individual systems exchange only relative information.

We will consider consensus and synchronization in networks of individual dynamical systems interconnected according to a specific communication topology, where the individual systems are modeled by ordinary differential equations and the communication topology is modeled by a graph. Typically, consensus problems deal with simple individual system dynamics and weak assumptions on the communication graph. In contrast, synchronization problems commonly focus on complex individual system dynamics and simple communication topologies. Very few results exist that consider complex individual systems and complex communication topologies at the same time. There seems to be tradeoff between admissible system complexity and admissible topological complexity in consensus and synchronization problems.

In view of this observation, we address two questions in this thesis. Firstly, we ask for the reasons for this tradeoff, i.e., we ask for the limitations that are inherent to static diffusive couplings. Secondly, we ask to what extent these limitations can be removed by appropriately extending static diffusive couplings.

We show that weak assumptions on the communication graph yield strong requirements imposed on the acting and sensing capabilities of the individual systems as well as their stability properties. On top of this tradeoff between system and topological complexity, static diffusive couplings are generally not suited to achieve consensus or synchronization if the individual systems admit non-identical dynamical models.

We propose diffusive couplings that are extended by dynamic compensators to overcome some of the aforementioned limitations of static diffusive couplings.

Strong requirements on the sensing capabilities are partly removed with the help of dynamic observers. The observer design problem for consensus problems is addressed subject to a relative sensing constraint in this thesis. We explain that this constraint yields a state estimation problem with unknown inputs and propose a solution based on unknown-input observers.

In case of heterogeneous networks, we show that an internal model principle is necessary for consensus and synchronization. We argue that this principle can generally only be satisfied if dynamic couplings are employed. The internal model principle derived in this thesis is related and compared to the theory of output regulation with its well-known internal model principle of control theory. Thereby we establish a link between consensus and synchronization on the one hand and the theory of output regulation on the other hand.

Eventually, we are able to give solutions to consensus and synchronization problems for arbitrary heterogeneous linear networks and for networks of heterogeneous nonlinear oscillators. We thereby remove most of the limitations mentioned above and thus allow for consensus and synchronization in networks with increased system and topological complexity.

Feedforward and feedback control of distributed parameter systems is a research area of great theoretical and practical interest. While several well-known methods exist to stabilize distributed parameter systems about stationary profiles, there are only very few efficient tools for feedforward and feedback tracking control design available for these systems.

This diploma thesis presents an easy to implement approach to compute feedforward control trajectories for distributed parameter systems as described by partial differential equations in time and space. The approach followed is based on a low-order approximation of the distributed parameter system using Galerkin's method. The feedforward task is then expressed in terms of an over-determined boundary value problem that can be solved by constructing the input trajectories including free parameters. A simple extension to the proposed approach is presented, that allows to incorporate input constraints directly in the formulation of the boundary value problem.

The proposed model-reduction and feedforward control design approaches are evaluated using different realistic tubular fixed bed reactor models as benchmark problems.

Making decisions is a crucial task that humans encounter in many situations. Especially in value management, where a large number of alternatives have to be ranked or weighted and where important economic values are at risk, one may want to be sure having taken a ``good'' decision. Pairwise comparison methods in combination with taking account of uncertainty by means of statistic simulation, provide reliable support for groups in taking such decisions. The abbreviation MCPC (Monte Carlo Pairwise Comparison) stands for a set of such routines, developped by M. Limayem and M. Yannou at the Ecole Centrale Paris.

The following document summarizes the project ``Collaborative Decision Making through Networks'' in German. Subject of the study was to determine ways how decsison making may take place (so called protocols) and propose a generalized vote model for spatially dispersed groups using MCPC. Attached are the complete project report in English and a formal description of the vote model.

the project was conducted in the ccontext of the TIME double-diploma-programme at the Ecole Centrale Paris under the surveillance of M. Yannou at the Laboratoire Génie Industriel of the Ecole Centrale Paris. M. Yannou's main axes of research are conceptual design and value analysis.